Mariano Giaquinta

Mariano Giaquinta's AcademicInfluence.com Rankings

Mariano Giaquinta

Mathematics

#6570

World Rank

#9077

Historical Rank

Applied Mathematics

#233

World Rank

#258

Historical Rank

Measure Theory

#1436

World Rank

#1801

Historical Rank

mathematics Degrees

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Mathematics

Mariano Giaquinta's Degrees

PhD Mathematics Scuola Normale Superiore di Pisa

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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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Mariano Giaquinta's Academic­Influence.com Rankings

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Why Is Mariano Giaquinta Influential?

Mariano Giaquinta's Published Works

Published Works

Mariano Giaquinta's AcademicInfluence.com Rankings