Mariano Giaquinta
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Applied Mathematics
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Mathematics
Mariano Giaquinta's Degrees
- PhD Mathematics Scuola Normale Superiore di Pisa
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(Suggest an Edit or Addition)Mariano Giaquinta'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
- Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 (1984) (1426)
- Cartesian currents in the calculus of variations (1983) (638)
- On the regularity of the minima of variational integrals (1982) (469)
- An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs (2005) (431)
- Introduction to Regularity Theory for Nonlinear Elliptic Systems (1993) (404)
- Growth conditions and regularity, a counterexample (1987) (210)
- Remarks on the regularity of the minimizers of certain degenerate functionals (1986) (199)
- On the partial regularity of weak solutions of nonlinear parabolic systems (1982) (197)
- One-dimensional variational problems : an introduction (1998) (193)
- Partial regularity of minimizers of quasiconvex integrals (1986) (155)
- Multiple integrals in the calculus of variations and non linear elliptic systems (1981) (146)
- Calculus of Variations I (1995) (145)
- Researches on the equilibrium of masonry structures (1985) (134)
- Functionals with linear growth in the calculus of variations. I. (1979) (133)
- One-dimensional Variational Problems (1998) (116)
- Existence of the displacements field for an elasto-plastic body subject to Hencky's law and Von Mises yield condition (1980) (114)
- The singular set of the minima of certain quadratic functionals (1984) (111)
- Non linear systems of the type of the stationary Navier-Stokes system. (1982) (111)
- Nonlinear elliptic systems with quadratic growth (1978) (101)
- Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity (1989) (100)
- Differentiability of minima of non-differentiable functionals (1983) (100)
- Cartesian currents and variational problems for mappings into spheres (1989) (89)
- Almost-everywhere regularity results for solutions of non linear elliptic systems (1979) (80)
- Convex functionals and partial regularity (1988) (80)
- Chapter I: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems (1984) (76)
- Mathematical Analysis: An Introduction to Functions of Several Variables (2004) (72)
- On the dirichlet problem for surfaces of prescribed mean curvature (1974) (72)
- A priori estimates for harmonic mappings. (1982) (71)
- The dirichlet energy of mappings with values into the sphere (1989) (65)
- Partial regularity for the solutions to nonlinear parabolic systems (1973) (64)
- Calculus of Variations II (2006) (61)
- Variational problems for maps of bounded variation with values inS1 (1993) (56)
- Global C1,α-regularity for second order quasilinear elliptic euqations in divergence form. (1984) (51)
- The BV-energy of maps into a manifold: relaxation and density results (2006) (51)
- A counter-example to the boundary regularity of solutions to elliptic quasilinear systems (1978) (50)
- Local existence for quasilinear parabolic systems under nonlinear boundary conditions (1987) (49)
- An optimal regularity result for a class of quasilinear parabolic systems (1981) (38)
- The Lagrangian formalism (1996) (37)
- Liquid crystals : relaxed energies, dipoles, singular lines and singular points (1990) (31)
- Erratum and addendum to “Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity”, this archive, volume 106 (1989): 97–159 (1990) (30)
- Maps of Bounded Variation with Values into a Manifold: Total Variation and Relaxed Energy (2007) (30)
- Area and the area formula (1992) (27)
- The Hamiltonian formalism (1996) (25)
- Caccioppoli's inequality and Legendre-Hadamard condition (1985) (25)
- The Dirichlet integral for mappings between manifolds: Cartesian currents and homology (1992) (25)
- Harmonic maps into a hemisphere (1985) (24)
- Graphs of finite mass which cannot be approximated in area by smooth graphs (1993) (24)
- Remarks on the regularity of weak solutions to some variational inequalities (1981) (23)
- Mathematical Analysis: Linear and Metric Structures and Continuity (2004) (21)
- On sequences of maps with equibounded energies (2001) (20)
- Quasiconvexity, growth conditions and partial regularity (1988) (19)
- Remarks on the Degree Theory (1994) (16)
- The gap phenomenon for variational integrals in Sobolev spaces (1992) (16)
- Hilbert space methods (2012) (14)
- Ground states of simple bodies that may undergo brittle fractures (2010) (14)
- The Early Period of the Calculus of Variations (2016) (13)
- A weak approach to finite elasticity (1994) (13)
- On the regularity of weak solutions to nonlinear elliptic systems via Liouville's type property (1979) (13)
- On sequences of maps into a manifold with equibounded W1/2-energies (2005) (12)
- Partial regularity for minima of variational integrals (1987) (11)
- Topics in Calculus of Variations (1989) (11)
- A variational problem in the mechanics of complex materials (2010) (10)
- On sequences of maps into S1 with equibounded W1/2 energies (2004) (10)
- On the regularity up to the boundary for second order nonlinear elliptic systems. (1982) (9)
- Mathematical analysis : functions and advanced techniques for functions of several variables (2012) (9)
- Density results for the W1/2 energy of maps into a manifold (2005) (9)
- The relaxed Dirichlet energy of manifold constrained mappings (2008) (9)
- Geometric theory of singular phenomena in partial differential equations, Cortona 1995 (1998) (9)
- Mathematical Analysis: Functions of One Variable (2003) (8)
- A new approximation of relaxed energies for harmonic maps and the Faddeev model (2009) (7)
- Partial regularity of minimizers of a functional involving forms and maps (2004) (7)
- Density results relative to the Dirichlet energy of mappings into a manifold (2006) (6)
- The Dirichlet energy of mappings from ${\bf B^3}$ into a manifold: density results and gap phenomenon (2004) (6)
- Weak and strong density results for the Dirichlet energy (2004) (6)
- Partial Regularity of Cartesian Currents which Minimize Certain Variational Integrals (1989) (6)
- Stress constraints in simple bodies undergoing large strains: a variational approach (2015) (5)
- On the self-length of two-dimensional Banach spaces (1996) (5)
- Partial regularity of minimizers (1986) (5)
- On the regularity of weak solutions to non linear elliptic systems of partial differential equations. (1980) (5)
- Relaxation results for a class of functionals with linear growth defined on manifold constrained mappings (2006) (4)
- The Regularity Problem of Extremals of Variational Integrals (1983) (4)
- The relaxed Dirichlet energy of mappings into a manifold (2005) (4)
- Mathematical Analysis: Approximation and Discrete Processes (2004) (4)
- On a relation between stochastic integration and geometric measure theory (2002) (4)
- Regular Variational Integrals (1998) (3)
- L2-regularity: The Caccioppoli inequality (2012) (3)
- Measures and Integration (2012) (3)
- The Brachistochrone Problem: Johann and Jakob Bernoulli (2016) (2)
- Cartesian Currents and Liquid Crystals Dipoles, Singular Lines and Singular Points (1991) (2)
- Differential Equations: La Pietra 1996 (1998) (2)
- Differential equations : La Pietra 1996 : Conference on Differential Equations marking the 70th birthdays of Peter Lax and Louis Nirenberg, July 3-7, 1996, Villa La Pietra, Florence, Italy (1999) (2)
- Remarks on the lower semicontinuity of quasiconvex integrals (1995) (2)
- Connectivity properties of the range of a weak diffeomorphism (1995) (2)
- Stratified energies: ground states with cracks (2009) (1)
- Topics in calculus of variations : lectures given at the 2nd 1987 session of the Centro internazionale matematico estivo (C.I.M.E.) held at Montecatini Terme, Italy, July 20-28, 1987 (1989) (1)
- On differentiability of the extremals of variational integrals (1982) (1)
- Some Regularity Properties of Locally Weakly Invertible Maps (1998) (1)
- Some remarks on the regularity of minimizers (1988) (1)
- Polynomials, Rational Functions and Trigonometric Polynomials (2004) (1)
- W 1 / 2-maps into S 1 and currents (2005) (1)
- Graphs of $W^{1,1}$-maps with values in $S^{1}$: relaxed energies, minimal connections and lifting (2007) (1)
- An extended propositional logic for incomplete knowledge (2011) (1)
- Mathematics in the social sciences: reflections on the theory of social choice and welfare (2015) (1)
- Weierstrass Field Theory for One-Dimensional Integrals and Strong Minimizers (2004) (1)
- Chapter IX: Direct Methods for the Regularity (1984) (0)
- Second Variation, Excess Function, Convexity (2004) (0)
- Composition of weak diffeomorphisms (1997) (0)
- Chapter VIII: A Few Remarks and Extensions (1984) (0)
- Minimizing Variational Integrals Among Diffeomorphisms (1990) (0)
- AN EXTENDED PROPOSITIONAL LOGIC (2014) (0)
- Legendre Transformation, Hamiltonian Systems, Convexity, Field Theories (2004) (0)
- Convex Sets and Convex Functions (2012) (0)
- Variational Problems with Subsidiary Conditions (2004) (0)
- Some remarks about the p-Dirichlet integral* (1994) (0)
- Parametric Variational Integrals (2004) (0)
- Euler’s Memoirs of 1738 and 1741 (2016) (0)
- Shortest Lines and Geodesics (2016) (0)
- Limits and Continuity (2003) (0)
- General Variational Formulas (2004) (0)
- Mathematical Analysis (2004) (0)
- Partial Differential Equations of First Order and Contact Transformations (2004) (0)
- The Fundamental Ideas of the Differential and Integral Calculus (2003) (0)
- Finite Elasticity and Weak Diffeomorphisms (1998) (0)
- Quadratic Functions and Partial Regularity (1985) (0)
- Some Regular and Non Regular Variational Problems (1998) (0)
- Surfaces and Level Sets (2009) (0)
- The First Variation (2004) (0)
- The Non Parametric Area Functional (1998) (0)
- The Calculus of Derivatives and of Integrals (2003) (0)
- Chapter II: An Introduction to the Regularity Problem (1984) (0)
- Analytic and Geometric Aspects of Variational Problems for Vector Valued Mappings (1994) (0)
- Regularity of the minima in the calculus of variations (1986) (0)
- Spaces of Summable Functions and Partial Differential Equations (2012) (0)
- Systems of Ordinary Differential Equations (2009) (0)
- The regularity problem in the scalar case (2012) (0)
- A survey of minimal graphs (2012) (0)
- Numbers, Functions and their Graphs (2003) (0)
- L p -theory (2012) (0)
- Chapter IV: Systems in Variation: The Indirect Approach to the Regularity (1984) (0)
- Chapter 1 Stratified Energies : Ground States with Cracks (2008) (0)
- V for Variations (2017) (0)
- Regularity results for weak solutions to variational equations and inequalitiesfor nonlinear elliptic systems and for weak solutions to nonlinear parabolicsystems (1980) (0)
- Curves and Differential Forms (2009) (0)
- Chapter VII: Nonlinear Elliptic Systems: Special Structures and Everywhere Regularity (1984) (0)
- Chapter V: Reverse Holder Inequalities And LP-Estimates (1984) (0)
- Compositions of weak diffeomorphisms (1997) (0)
- NONLINEAR ELLIPTIC SYSTEMS WITH (1978) (0)
- Toward Differential Equations and Minimum Principles (2003) (0)
- Hamilton-Jacobi Theory and Canonical Transformations (2004) (0)
- The Dirichlet Energy for Maps into the Two Dimensional Sphere (1998) (0)
- Sequences of Real Numbers (2004) (0)
- The Dirichlet Integral in Sobolev Spaces (1998) (0)
- Weak Minimizers and Jacobi Theory (2004) (0)
- The Formalism of the Calculus of Variations (2012) (0)
- Singular Perturbations Associated to the Dirichlet Energy of Maps with Values in S2 (1993) (0)
- Isoperimetrical Problems: Jakob and Johann Bernoulli (2016) (0)
- Further Developments in Calculus (2003) (0)
- Integer Numbers: Congruences, Counting and Infinity (2004) (0)
- Hausdorff and Radon Measures (2012) (0)
- Partial regularity in the vector-valued case (2012) (0)
- Chapter III: Linear Systems: The Regularity Theory (1984) (0)
- Chapter VI: Nonlinear Elliptic Systems: The Direct Approach to Regularity (1984) (0)
- Some real analysis (2012) (0)
- Real Numbers and Natural Numbers (2004) (0)
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