Giuseppe Mingione | Academic Influence

Giuseppe Mingione's AcademicInfluence.com Rankings

Giuseppe Mingione

Mathematics

#1613

World Rank

#2610

Historical Rank

Measure Theory

#268

World Rank

#423

Historical Rank

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Mathematics

Giuseppe Mingione's Degrees

PhD Mathematics University of Pavia
Masters Mathematics University of Pavia
Bachelors Mathematics University of Pavia

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Why Is Giuseppe Mingione Influential?

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According to Wikipedia, Giuseppe Mingione is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations. Scientific activity Mingione received his Ph.D. in mathematics from the University of Naples Federico II in 1999 having Nicola Fusco as advisor; he is professor of mathematics at the University of Parma. He has mainly worked on regularity aspects of the Calculus of Variations, solving a few longstanding questions about the Hausdorff dimension of the singular sets of minimisers of vectorial integral functionals and the boundary singularities of solutions to nonlinear elliptic systems. This connects to the work of authors as Almgren, De Giorgi, Morrey, Giusti, who proved theorems asserting regularity of solutions outside a singular set both in geometric measure theory and for variational systems of partial differential equations. These are indeed called partial regularity results and one of the main issues is to establish whether the dimension of the singular set is strictly less than the ambient dimension. This question has found a positive answer for general integral functionals, thanks to the work of Kristensen and Mingione, who have also given explicit estimates for the dimension of the singular sets of minimisers. Subsequently, Mingione has worked on nonlinear potential theory obtaining potential estimates for solutions to nonlinear elliptic and parabolic equations. Such estimates allow to give a unified approach to the regularity theory of quasilinear, degenerate equations and relate to and upgrade previous work of Kilpeläinen, Malý, Trudinger, Wang.

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Giuseppe Mingione'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

Regularity Results for Stationary Electro-Rheological Fluids (2002) (622)
Regularity Results for a Class of Functionals with Non-Standard Growth (2001) (524)
Gradient estimates for a class of parabolic systems (2007) (404)
Gradient estimates for the p (x)-Laplacean system (2005) (402)
Regularity of minima: An invitation to the dark side of the calculus of variations (2006) (399)
Bounded Minimisers of Double Phase Variational Integrals (2015) (362)
The Calderón-Zygmund theory for elliptic problems with measure data (2006) (329)
Regularity for general functionals with double phase (2017) (320)
Sharp regularity for functionals with (p,q) growth (2004) (301)
Regularity for Double Phase Variational Problems (2015) (275)
Harnack inequalities for double phase functionals (2015) (247)
Gradient estimates via non-linear potentials (2009) (243)
Gradient estimates below the duality exponent (2010) (242)
Non-autonomous functionals, borderline cases and related function classes (2016) (230)
Calderón–Zygmund estimates and non-uniformly elliptic operators (2016) (203)
Gradient potential estimates (2011) (202)
Hölder continuity of the gradient of p(x)-harmonic mappings (1999) (195)
Universal potential estimates (2012) (189)
Guide to nonlinear potential estimates (2014) (189)
The Singular Set of Minima of Integral Functionals (2006) (189)
Nonlocal Equations with Measure Data (2014) (179)
Regularity results for parabolic systems related to a class of non-Newtonian fluids (2004) (174)
Gradient estimates via linear and nonlinear potentials (2010) (163)
Parabolic systems with polynomial growth and regularity (2011) (150)
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021) (139)
The Singular Set of Solutions to Non-Differentiable Elliptic Systems (2003) (138)
Degenerate problems with irregular obstacles (2011) (132)
Regularity results for electrorheological fluids: the stationary case (2002) (124)
Regularity results for minimizers of irregular integrals with (p,q) growth (2002) (122)
Boundary Regularity in Variational Problems (2010) (120)
The p-harmonic approximation and the regularity of p-harmonic maps (2004) (118)
Lipschitz Bounds and Nonuniform Ellipticity (2019) (118)
Partial regularity of minimizers of quasiconvex integrals with subquadratic growth (1998) (118)
Regularity results for a class of quasiconvex functionals with nonstandard growth (2001) (115)
Nonlocal self-improving properties (2015) (113)
Second order parabolic systems, optimal regularity, and singular sets of solutions (2005) (109)
Linear Potentials in Nonlinear Potential Theory (2013) (107)
Vectorial nonlinear potential theory (2018) (103)
The Wolff gradient bound for degenerate parabolic equations (2014) (103)
The Regularity of General Parabolic Systems With Degenerate Diffusion (2012) (96)
Full C1,α-regularity for free and constrained local minimizers of elliptic variational integrals¶with nearly linear growth (2000) (93)
Scalar Minimizers with Fractal Singular Sets (2004) (92)
Regularity for minimizers of functionals with p – q growth (1999) (89)
Gradient continuity estimates (2010) (89)
Local Lipschitz regularity for degenerate elliptic systems (2009) (89)
Higher Integrability for Minimizers of Integral Functionals With (p, q) Growth (1999) (87)
Gradient regularity for elliptic equations in the Heisenberg group (2007) (80)
The Singular Set of Lipschitzian Minima of Multiple Integrals (2007) (78)
Nonlinear Calderón–Zygmund Theory in the Limiting Case (2018) (78)
Regularity for degenerate elliptic problems via p-harmonic approximation (2004) (78)
Bounds for the singular set of solutions to non linear elliptic systems (2003) (78)
Gradient regularity for nonlinear parabolic equations (2013) (74)
Regularity results for quasilinear elliptic equations in the Heisenberg group (2007) (71)
Ice Accretion Prediction on Multielement Airfoils (1998) (69)
On the Regularity of Minima of Non-autonomous Functionals (2019) (68)
Riesz Potentials and Nonlinear Parabolic Equations (2013) (66)
Lipschitz Bounds and Nonautonomous Integrals (2020) (65)
Manifold Constrained Non-uniformly Elliptic Problems (2019) (64)
Partial continuity for elliptic problems (2008) (64)
The existence of regular boundary points for non-linear elliptic systems (2007) (63)
A nonlinear Stein theorem (2014) (61)
Nonlinear Measure Data Problems (2011) (56)
New perturbation methods for nonlinear parabolic problems (2012) (55)
The Singular Set of ω-minima (2005) (55)
The boundary regularity of non-linear parabolic systems I (2010) (52)
Singularities of minima: a walk on the wild side of the Calculus of Variations (2008) (50)
Harmonic type approximation lemmas (2009) (43)
Potential estimates and gradient boundedness for nonlinear parabolic systems (2012) (42)
Full $C^{1, \alpha}$-Regu1arity for Minimizers of Integral Functionals with $L$ log $L$-Growth (1999) (37)
Borderline gradient continuity of minima (2014) (36)
On the Lipschitz regularity for certain elliptic problems (2006) (36)
Elliptic Systems, Singular Sets and Dini Continuity (2004) (36)
Development and evaluation of poly(dimethylsiloxane) based composite coatings for icephobic applications (2018) (35)
Integral Functionals and the Gap Problem: Sharp Bounds for Relaxation and Energy Concentration (2005) (34)
Borderline Estimates for Fully Nonlinear Elliptic Equations (2012) (33)
A Priori Gradient Bounds and Local $C^{1, \alpha}$-Estimates for (Double) Obstacle Problems under Non-Standard Growth Conditions (2001) (33)
A borderline case of Calder\'on-Zygmund estimates for non-uniformly elliptic problems (2019) (32)
Nonlinear Aspects of Calderón-Zygmund Theory (2010) (32)
Partial Regularity for Minimizers of Degenerate Polyconvex Energies (2001) (29)
Partial regularity of local minimizers of quasiconvex integrals with sub-quadratic growth (2003) (29)
Partial regularity for minimizers of convex integrals with L log L-growth (2000) (28)
Eulerian Modeling of Large Droplet Physics Toward Realistic Aircraft Icing Simulation (2011) (27)
Ice accretion prediction on multi-element airfoils (1997) (27)
A fractional Gehring lemma, with applications to nonlocal equations (2014) (26)
Some remarks on the regularity of weak solutions of degenerate elliptic systems (1998) (24)
NONLINEAR POTENTIAL ESTIMATES IN PARABOLIC PROBLEMS (2011) (24)
Gradient regularity in mixed local and nonlocal problems (2022) (22)
Water Impingement Prediction on Multi-Element Airfoils by Means of Eulerian and Lagrangian Approach with Viscous and Inviscid Air Flow (2006) (22)
A surprising linear type estimate for nonlinear elliptic equations (2011) (21)
Developments and perspectives in Nonlinear Potential Theory (2020) (21)
Existence and regularity for mixtures of micromagnetic materials (2006) (20)
Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets (2014) (20)
Gradient estimates in non-linear potential theory (2009) (19)
Mission Trade-Off Analysis of the Italian USV Re-Entry Flying Test Bed (2006) (18)
Ice Accretion Model on Multi-Element Airfoil (2010) (17)
Borderline gradient continuity for nonlinear parabolic systems (2014) (17)
Calderón–Zygmund estimates for measure data problems (2007) (16)
Regularity in parabolic systems with continuous coefficients (2012) (16)
Non-differentiable functionals and singular sets of minima (2005) (16)
Partial regularity and potentials (2016) (14)
A 3D ice accretion simulation code (1999) (13)
A Boundary Harnack Inequality for Singular Equations of p-Parabolic Type (2014) (12)
FLUIDS WITH PRESSURE DEPENDENT VISCOSITY: PARTIAL REGULARITY OF STEADY FLOWS (2005) (12)
Regularity of Minimizers for a Class of Anisotropic Free Discontinuity Problems (2001) (12)
TOWARDS A NON-LINEAR CALDER ON-ZYGMUND THEORY (2009) (11)
Interpolative gap bounds for nonautonomous integrals (2021) (11)
EXTICE: EXTreme Icing Environement (2011) (10)
Ice Accretion Prediction on Helicopter Rotor Blade in Hover Flight (2007) (10)
Prediction of Ice Accumulation and Airfoil Performance Degradation: A Boeing - CIRA Research Collaboration (2006) (10)
CIRAAMIL Ice Accretion Code Improvements (2009) (9)
Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions - Cetraro, Italy (2017) (9)
Beads and rivulets modeling in ice accretion on a wing (1998) (9)
Boundary regularity of minima (2008) (9)
EURICE: an European effort for the improvement of in-flight aircraft icing safety (1998) (8)
Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems (2018) (8)
On the problem of icing for modern civil aircraft (2001) (8)
Nonlinear Potential Theory of elliptic systems (2016) (8)
The Singular Set of omega-minima (2005) (7)
Airframe Noise Reduction Technologies applied to High-Lift Devices of Future Green Regional Aircraft (2014) (7)
Functionals with $p(x)$ growth and regularity (2000) (7)
Relaxation results for higher order integrals below the natural growth exponent (2002) (6)
Assessment of Flap Side-Edge Fence Noise using SNGR Method (2015) (6)
CIRAAMIL Ice Accretion Code Improvement (2009) (6)
Pointwise gradient estimates (2012) (6)
Short Tales from Nonlinear Calderón-Zygmund Theory (2017) (6)
Regularity Issues Involving the Fractional p-Laplacian (2017) (6)
Nonlinear Aspects of Caldern-Zygmund Theory (2010) (5)
Nonuniformly elliptic Schauder theory (2022) (5)
Sketches of Regularity Theory from The 20 th Century and the Work of Jindrich Necas (2011) (5)
Eulerian modeling of SLD physics towards more realistic aircraft icing simulation (2010) (5)
Higher differentiability for minimizers of irregular integrals (2001) (4)
Riesz Potentials and Nonlinear Parabolic Equations (2013) (4)
Topics in Modern Regularity Theory (2012) (4)
Partial regularity of minimizers of quasiconvex integrals with subquadratic growth: the general case (2001) (4)
Installation issues of a small turboshaft engine into a light helicopter (2015) (3)
Endpoint and Intermediate Potential Estimates for Nonlinear Equations (2011) (3)
On the Regularity of p-Harmonic Functions in the Heisenberg Group (2008) (3)
Experimental and computational aerodynamics applications for an icing wind tunnel design (1997) (3)
Recent Advances in Nonlinear Potential Theory (2014) (3)
An Eulerian approach to three-dimensional droplet impingement simulation in icing environment (2010) (3)
GRADIENT ESTIMATES VIA NON-LINEAR POTENTIALS By FRANK DUZAAR and GIUSEPPE MINGIONE (2011) (2)
On the continuity of the solution of the singular equation (B( u )) =D u (1999) (2)
Assessment of Conceptual Noise Reduction Devices for A Main Landing Gear using SNGR Method (2015) (2)
Regularity in parabolic systems with continuous coefficients (2011) (2)
CFD analysis of a coupled Bleed Air and Electrothermal icing protection system (2017) (1)
Numerical procedure for electro-thermal anti-icing system simulation coupling internal thermal analysis and external multi-physic code (2021) (1)
Linear Potentials in Nonlinear Potential Theory (2012) (1)
Validation of Liquid Water Content Simulation using the Film Thickness at Stagnation Point (2018) (1)
Manifold Constrained Non-uniformly Elliptic Problems (2019) (1)
SKETCHES OF NONLINEAR CALDERÓN-ZYGMUND THEORY (2011) (1)
On the Regularity of Minima of Non-autonomous Functionals (2019) (0)
Carlo Sbordone, a Neapolitan mathematician (2018) (0)
A nonlinear Stein theorem (2013) (0)
Application of different Lagrangian Particle Tracking techniques for water impingement (2021) (0)
Parametric Studies and Simulations of a Hydrogen Micromix Combustor (2022) (0)
The various stages of Nicola Fusco (2017) (0)
Numerical investigation of the internal and external thermal fields for a nacelle in pusher configuration (2017) (0)
Borderline gradient continuity for nonlinear parabolic systems (2014) (0)
Adaptive Structures for Noise and Vibration Guidance, Monitoring and Control (2023) (0)
Nonlocal Equations with Measure Data (2015) (0)
[Histopathological classification of epithelial neoplasms of the bladder as a means of comparison for cytological diagnosis]. (1974) (0)
Calcolo delle variazioni . — Functionals with p ( x ) growth and regularity (2013) (0)
Editorial (0)
The various stages of Nicola Fusco (Part 2) (2017) (0)
ON AN EIGENVALUE PROBLEM INVOLVING THE p(x)–LAPLACE OPERATOR PLUS A NON–LOCAL TERM (2009) (0)
Regularity for Double Phase Variational Problems (2014) (0)
Bounded Minimisers of Double Phase Variational Integrals (2015) (0)
Preface [6th European Conference on Elliptic and Parabolic Problems]. Held in Gaeta, May 25–29, 2009. (2010) (0)
Borderline gradient continuity of minima (2014) (0)
Regularity for general functionals with double phase (2018) (0)
Applications of Mathematics (2006) (0)
The Weiss – Landau – Lifschitz model for one crystal briefly visited (2006) (0)
()N THE CONTINUITY OF THE SOLUTION OF THE SINGULAR EQUATION (BETA (U))T = DELTA U (1999) (0)
Parametric Investigation of a Distributed Propulsion System on a Regional Aircraft (2022) (0)
WITHDRAWN: Carlo Sbordone, a Neapolitan mathematician (2018) (0)
Nonlinear Calderón–Zygmund Theory in the Limiting Case (2017) (0)
Landing gear noise reduction technology development for future green regional aircraft (2014) (0)

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