Eduardo Casas-Alvero
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Spanish mathematician
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Eduardo Casas-Alveromathematics Degrees
Mathematics
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Group Theory
#154
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#185
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Number Theory
#282
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Algebra
#373
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#520
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Mathematics
Eduardo Casas-Alvero's Degrees
- PhD Mathematics University of Barcelona
- Masters Mathematics University of Barcelona
- Bachelors Mathematics University of Barcelona
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Why Is Eduardo Casas-Alvero Influential?
(Suggest an Edit or Addition)According to Wikipedia, Eduardo Casas-Alvero is a Spanish mathematician and a professor at the University of Barcelona. His work lies in algebraic geometry and commutative algebra, especially curve theory. One of his main contributions has been the Casas-Alvero conjecture characterizing certain polynomials whose factors match their derivatives as powers of a linear polynomial.
Eduardo Casas-Alvero's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Control of an elliptic problem with pointwise state constraints (1986) (320)
- Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem (2002) (283)
- Pontryagin's Principle for State-Constrained Boundary Control Problems of Semilinear Parabolic Equations (1997) (278)
- Boundary control of semilinear elliptic equations with pointwise state constraints (1993) (256)
- Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations (2006) (169)
- Sufficient Second-Order Optimality Conditions for Semilinear Control Problems with Pointwise State Constraints (2008) (142)
- Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems (2005) (138)
- Approximation of Elliptic Control Problems in Measure Spaces with Sparse Solutions (2012) (125)
- Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with L1 Cost Functional (2012) (109)
- Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations (2000) (107)
- UNIFORM CONVERGENCE OF THE FEM. APPLICATIONS TO STATE CONSTRAINED CONTROL PROBLEMS (2002) (107)
- Second-Order Necessary and Sufficient Optimality Conditions for Optimization Problems and Applications to Control Theory (2002) (106)
- Second Order Optimality Conditions for Semilinear Elliptic Control Problems with Finitely Many State Constraints (2001) (102)
- Parabolic Control Problems in Measure Spaces with Sparse Solutions (2013) (97)
- Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints (2002) (92)
- An Extension of Pontryagin's Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities (1995) (91)
- L2 estimates for the finite element method for the Dirichlet problem with singular data (1985) (90)
- Second Order Optimality Conditions and Their Role in PDE Control (2015) (85)
- Second Order Analysis for Optimal Control Problems: Improving Results Expected From Abstract Theory (2012) (83)
- Second Order Analysis for Bang-Bang Control Problems of PDEs (2012) (82)
- Regularization by Functions of Bounded Variation and Applications to Image Enhancement (1999) (79)
- Error estimates for linear-quadratic elliptic control problems (2002) (77)
- Sparse Optimal Control of the Schlögl and FitzHugh–Nagumo Systems (2013) (76)
- Pontryagin's Principle For Local Solutions of Control Problems with Mixed Control-State Constraints (2000) (73)
- Error Estimates for the Numerical Approximation of a Distributed Control Problem for the Steady-State Navier--Stokes Equations (2007) (72)
- Error estimates for the finite-element approximation of a semilinear elliptic control problem (2002) (70)
- Optimal Control of Partial Differential Equations (2017) (70)
- First- and Second-Order Optimality Conditions for a Class of Optimal Control Problems with Quasilinear Elliptic Equations (2009) (70)
- Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems (2007) (69)
- Error estimates for the numerical approximation of Neumann control problems (2008) (69)
- Distributed Control of Systems Governed by a General Class of Quasilinear Elliptic Equations (1993) (66)
- Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations (1999) (64)
- A Green's formula for quasilinear elliptic operators (1989) (62)
- Penalization of Dirichlet optimal control problems (2009) (61)
- Optimal control of semilinear multistate systems with state constraints (1989) (59)
- Second Order Sufficient Optimality Conditions for a Nonlinear Elliptic Boundary Control Problem (1996) (55)
- Some optimal control problems of multistate equations appearing in fluid mechanics (1993) (54)
- Second Order and Stability Analysis for Optimal Sparse Control of the FitzHugh-Nagumo Equation (2015) (53)
- Approximation of sparse controls in semilinear equations by piecewise linear functions (2012) (53)
- New regularity results and improved error estimates for optimal control problems with state constraints (2014) (51)
- Optimal control in coefficients of elliptic equations with state constraints (1992) (48)
- Optimal Control of Semilinear Elliptic Equations in Measure Spaces (2014) (46)
- Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state (1993) (46)
- Parabolic control problems in space-time measure spaces (2016) (46)
- Spike controls for elliptic and parabolic PDEs (2013) (46)
- Sparse initial data identification for parabolic PDE and its finite element approximations (2015) (46)
- Analysis of Spatio-Temporally Sparse Optimal Control Problems of Semilinear Parabolic Equations (2017) (45)
- Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic (1995) (42)
- A general theorem on error estimates with application to a quasilinear elliptic optimal control problem (2012) (38)
- Approximation of Optimal Control Problems in the Coefficient for the p-Laplace Equation. I. Convergence Result (2016) (33)
- On the choice of the function spaces for some state-constrained control problems (1985) (30)
- RECENT ADVANCES IN THE ANALYSIS OF POINTWISE STATE-CONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS ∗ (2010) (28)
- Second-Order Optimality Conditions for Weak and Strong Local Solutions of Parabolic Optimal Control Problems (2016) (27)
- A Discontinuous Galerkin Time-Stepping Scheme for the Velocity Tracking Problem (2012) (27)
- Sufficient Second-Order Conditions for Bang-Bang Control Problems (2017) (27)
- Analysis of the Velocity Tracking Control Problem for the 3D Evolutionary Navier-Stokes Equations (2016) (26)
- Optimal control of quasilinear parabolic equations (1995) (26)
- Second-Order and Stability Analysis for State-Constrained Elliptic Optimal Control Problems with Sparse Controls (2014) (25)
- Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems (2017) (25)
- Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity (1998) (24)
- Finite element approximation of sparse parabolic control problems (2017) (24)
- Optimal Control of Semilinear Parabolic Equations by BV-Functions (2017) (24)
- Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints (2008) (23)
- 4. An Optimal Control Problem Governed by the Evolution Navier-Stokes Equations (1998) (23)
- Approximation of boundary control problems on curved domains (2009) (23)
- NUMERICAL ANALYSIS OF SOME OPTIMAL CONTROL PROBLEMS GOVERNED BY A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS (2011) (23)
- Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations (2012) (21)
- Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations (2008) (20)
- Pontryagin’s Principle for Optimal Control Problems Governed by Semilinear Elliptic Equations (1994) (19)
- Pontryagin's principle for the control of parabolic equations with gradient state constraints (2001) (19)
- Optimality Conditions for Some Control Problems of Turbulent Flows (1995) (19)
- Analysis and optimal control of some quasilinear parabolic equations (2018) (18)
- A boundary Pontryagin’s principle for the optimal control of state-constrained elliptic systems (1992) (18)
- Some applications of BV functions in optimal controls and calculus of variations (1998) (17)
- Dealing with Integral State Constraints in BoundaryControl Problems of Quasilinear Elliptic Equations (1995) (16)
- Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity (2018) (16)
- Error Estimates for Semilinear Parabolic Control Problems in the Absence of Tikhonov Term (2019) (16)
- A Paradox in the Approximation of Dirichlet Control Problems in Curved Domains (2011) (15)
- Critical Cones for Sufficient Second Order Conditions in PDE Constrained Optimization (2019) (14)
- An algorithm for indefinite quadratic programming based on a partial Cholesky factorization (1993) (14)
- The Stability in W s,p (Γ) Spaces of L 2-Projections on Some Convex Sets (2006) (14)
- Error estimates for the numerical approximation of a quaslinear Neumann problem under minimal regularity of the data (2011) (14)
- The relaxation theory applied to optimal control problems of semilinear elliptic equations (1996) (14)
- Stabilization by Sparse Controls for a Class of Semilinear Parabolic Equations (2017) (13)
- Spike Controls for Elliptic and Parabolic PDE (2013) (12)
- Error estimates for the discretization of the velocity tracking problem (2015) (12)
- Optimal control of quasilinear elliptic equations (1989) (11)
- Boundary control problems for quasi-linear elliptic equations: (1996) (11)
- A review on sparse solutions in optimal control of partial differential equations (2017) (10)
- Numerical approximation of elliptic control problems with finitely many pointwise constraints (2009) (10)
- Optimal Control Problem Governed by Semilinear Elliptic Equations with Integral Control Constraints and Pointwise State Constraints (1998) (10)
- Error estimates for the approximation of the velocity tracking problem with bang-bang controls (2017) (9)
- Optimal Control of Semilinear Parabolic Equations with Non-smooth Pointwise-Integral Control Constraints in Time-Space (2021) (9)
- On the singularities of polar curves (1983) (9)
- State Error Estimates for the Numerical Approximation of Sparse Distributed Control Problems in the Absence of Tikhonov Regularization (2021) (9)
- Analysis of Optimal Control Problems of Semilinear Elliptic Equations by BV-Functions (2017) (9)
- Approximation of Sparse Controls in Semilinear Elliptic Equations (2011) (8)
- Optimal control of a class of reaction–diffusion systems (2018) (8)
- Optimal Control of the Two-Dimensional Stationary Navier-Stokes Equations with Measure Valued Controls (2019) (7)
- Analysis of control problems of nonmontone semilinear elliptic equations (2019) (7)
- Using sparse control methods to identify sources in linear diffusion-convection equations (2019) (7)
- Dirichlet control problems in smooth and nonsmooth convex plain domains (2011) (7)
- Second-order optimality conditions for semilinear elliptic control problems with constraints on the gradient of the state (1999) (6)
- First and Second Order Conditions for Optimal Control Problems with an L0 Term in the Cost Functional (2020) (5)
- State-constrained semilinear elliptic optimization problems with unrestricted sparse controls (2020) (5)
- Optimal Control of PDE Theory and Numerical Analysis (2006) (5)
- Numerical analysis of quasilinear parabolic equations under low regularity assumptions (2019) (5)
- The Influence of the Tikhonov Term in Optimal Control of Partial Differential Equations (2018) (5)
- Maximum Principles in the Optimal Control of Semilinear Elliptic Systems (1989) (4)
- Optimal control of state-constrained unstable systems of elliptic type (1989) (4)
- Corrigendum: Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state (1993) (4)
- State-constrained control problems of quasilinear elliptic equations (1991) (4)
- Optimal Control of the 2D Evolutionary Navier-Stokes Equations with Measure Valued Controls (2020) (4)
- Moduli of algebroid plane curves (1982) (3)
- Sparse optimal control for the heat equation with mixed control-state constraints (2020) (3)
- Expansion of the current methodology for the study of the short-term liquidity problems in a sector (2018) (3)
- Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains (2020) (3)
- New assumptions for stability analysis in elliptic optimal control problems (2022) (3)
- Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations (2021) (3)
- A sequential generalized quadratic programming algorithm using exact L 1Penalty Functions (1993) (3)
- El número borroso triangular "ratio acid-test mínima" (2016) (2)
- Stability for Semilinear Parabolic Optimal Control Problems with Respect to Initial Data (2022) (2)
- Optimal time delays in a class of reaction-diffusion equations (2018) (2)
- Second order sufficient optimality conditions for a class of elliptic control problems (1998) (2)
- On Optimal Control Problems with Controls Appearing Nonlinearly in an Elliptic State Equation (2020) (2)
- Error estimates for the numerical approximation of optimal control problems with nonsmooth pointwise-integral control constraints (2022) (2)
- Fractional systems and optimization (2014) (2)
- Optimal Control of the Two-Dimensional Evolutionary Navier-Stokes Equations with Measure Valued Controls (2021) (2)
- Measure Control of a Semilinear Parabolic Equation with a Nonlocal Time Delay (2018) (1)
- A Note on Existence of Solutions to Control Problems of Semilinear Partial Differential Equations (2022) (1)
- Optimal control of PDEs and FE-approximation (2022) (1)
- Optimal control of quasilinear multistate elliptic systems (1988) (1)
- Infinite Horizon Optimal Control Problems for a Class of Semilinear Parabolic Equations (2021) (1)
- A general theorem on error estimates with application to a quasilinear elliptic optimal control problem (2012) (1)
- A Review of Numerical Analysis for the Discretization of the Velocity Tracking Problem (2016) (1)
- Some stability concepts and their applications in optimal control problems (1992) (1)
- Second Order Optimality Conditions for Some Control Problems of Semilinear Elliptic Equations with Integral State Constraints (1999) (1)
- Corrigendum: Critical Cones for Sufficient Second Order Conditions in PDE Constrained Optimization (2022) (1)
- Optimality conditions for state-constrained control problems of quasilinear elliptic equations (1991) (1)
- Recent Advances in the Analysis of State-constrained Elliptic Optimal Control Problems (2009) (1)
- Sparse optimal control for a semilinear heat equation with mixed control-state constraints – regularity of Lagrange multipliers (2020) (1)
- Numerical approximation of elliptic control problems with finitely many pointwise constraints (2011) (1)
- Control of partial differential equations and applications : proceedings of the IFIP TC7/WG-7.2 international conference, Laredo, Spain (1996) (0)
- Analytic Singular Perturbations of Elliptic Systems (1987) (0)
- Population dynamics, control and applications (2010) (0)
- Second-Order Optimality Conditions for Weak and Strong Local Solutions of Parabolic Optimal Control Problems (2015) (0)
- Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations (2011) (0)
- A review on sparse solutions in optimal control of partial differential equations (2017) (0)
- Dealing with degenerated cases in quadratic programming (1988) (0)
- Symposium on Optimal Control of Partial Differential Equations (2009) (0)
- Preface special issue on system modeling and optimization (2021) (0)
- Correction to: State Error Estimates for the Numerical Approximation of Sparse Distributed Control Problems in the Absence of Tikhonov Regularization (2022) (0)
- Optimal Control of Coupled Systems of PDE (2008) (0)
- Optimal Control of PDE (2009) (0)
- 1 4 M ay 2 01 9 Critical cones for sufficient second order conditions in PDE constrained optimization ∗ (2019) (0)
- Second Order Conditions for L 2 Local Optimality in PDE Control (2011) (0)
- Erratum to "well-poseness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains" (2022) (0)
- Analysis of Optimal Control Problems with an $L^0$ Term in the Cost Functional (2020) (0)
- Optimal control of a parabolic equation with memory (2023) (0)
- Using Sparse Control Methods to Identify Sources (2019) (0)
- Second Order Optimality Conditions and Their Role in PDE Control (2014) (0)
- Error estimates for the discretization of the velocity tracking problem (2014) (0)
- Exact penalization of pointwise constraints for optimal control problems (2009) (0)
- FIRST AND SECOND ORDER CONDITIONS FOR OPTIMAL CONTROL PROBLEMS WITH AN \bfitL TERM IN THE COST FUNCTIONAL\ast (2020) (0)
- Optimal Control of Semilinear Parabolic Equations with Non-smooth Pointwise-Integral Control Constraints in Time-Space (2022) (0)
- Approximation of sparse controls in semilinear equations by piecewise linear functions (2012) (0)
- O C ] 3 1 M ay 2 01 9 Analysis of control problems of nonmontone semilinear elliptic equations ∗ (2019) (0)
- Analysis of Optimal Control Problems of Semilinear Elliptic Equations by BV-Functions (2018) (0)
- ERRATUM TO ”WELL-POSEDNESS OF EVOLUTIONARY NAVIER-STOKES QUATIONS WITH FORCES OF LOW REGULARITY ON TWO-DIMENSIONAL DOMAINS” ESAIM: COCV, VOLUME 27, 2021 (2022) (0)
- Optimal control of a class of reaction–diffusion systems (2018) (0)
- Optimal control problems of quasilinear parabolic equations (1993) (0)
- Choosing L q controls to deal with pointwise state constraints (1992) (0)
- Preface: A tribute to Professor Enrique Zuazua on his 60th birthday (2021) (0)
- Error Estimates for the Numerical Approximation of Unregularized Sparse Parabolic Control Problems (2022) (0)
- Boundary Control of Semilinear Parabolic Equations with Non-Smooth Point-wise-Integral Control Constraints in Time-Space* (2022) (0)
- Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity (2018) (0)
- Strong Pontryagin’s principle for state-constrained control problems governed by parabolic equations (1996) (0)
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