Nonlinear potential theory of elliptic systems

DOI10.1016/j.na.2015.12.022zbMath1338.35194OpenAlexW2282545219WikidataQ58880695 ScholiaQ58880695MaRDI QIDQ272752

Tuomo Kuusi, Giuseppe Mingione

Publication date: 20 April 2016

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.12.022

zbMATH Keywords

regularityelliptic equations\(p\)-Laplaciannonlinear potential theory

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Other generalizations (nonlinear potential theory, etc.) (31C45) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items

Regularity estimates for quasilinear elliptic equations with variable growth involving measure data ⋮ The Calderón–Zygmund estimates for a class of nonlinear elliptic equations with measure data ⋮ Wolff potentials and measure data vectorial problems with Orlicz growth ⋮ A NOTE ON QUASILINEAR ELLIPTIC SYSTEMS WITH L^\infty-DATA ⋮ Quasilinear Lane-Emden type systems with sub-natural growth terms ⋮ Potential estimates for fully nonlinear elliptic equations with bounded ingredients ⋮ Quasilinear elliptic systems with right-hand side in divergence form ⋮ Borderline gradient estimates at the boundary in Carnot groups

Cites Work

• NON-LINEAR POTENTIAL THEORY
• Estimates for \(p\)-Poisson equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local approximation of superharmonic and superparabolic functions in nonlinear potential theory
• A nonlinear Stein theorem
• Universal potential estimates
• Potential estimates and gradient boundedness for nonlinear parabolic systems
• Borderline gradient continuity for nonlinear parabolic systems
• Elliptic systems with measure data
• Partial regularity and potentials
• Interior a priori estimates for solutions of fully nonlinear equations
• Gradient estimates via linear and nonlinear potentials
• Gradient continuity estimates
• Local Lipschitz regularity for degenerate elliptic systems
• Gradient potential estimates
• A surprising linear type estimate for nonlinear elliptic equations
• Nonlinear measure data problems
• Superharmonic functions are locally renormalized solutions
• Nonlinear elliptic equations in \(\mathbb{R}^ N\) without growth restrictions on the data
• Boundary regularity in variational problems
• Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\)
• Marcinkiewicz estimates for solutions of some elliptic problems with nonregular data
• Gradient estimates below the duality exponent
• Partial regularity for minimisers of certain functionals having nonquadratic growth
• Nonlinear elliptic and parabolic equations involving measure data
• Partial continuity for elliptic problems
• Regularity of minima: an invitation to the dark side of the calculus of variations.
• Singular quasilinear and Hessian equations and inequalities
• Remarks on the regularity of the minimizers of certain degenerate functionals
• Regularity for minima of functionals with p-growth
• Regularitätsuntersuchungen von Lösungen elliptischer Systeme von quasilinearen Differentialgleichungen zweiter Ordnung
• A note on Riesz potentials
• Regularity for a class of nonlinear elliptic systems
• Almost-everywhere regularity results for solutions of nonlinear elliptic systems
• The blow-up of \(p\)-harmonic maps
• The Wiener test and potential estimates for quasilinear elliptic equations
• The \(p\)-harmonic system with measure-valued right hand side
• Nonlinear parabolic equations with measure data
• Bounds for the singular set of solutions to non linear elliptic systems
• The singular set of solutions to non-differentiable elliptic systems
• Optimal interior partial regularity for nonlinear elliptic systems: The method of \(A\)-harmonic approximation
• Vectorial nonlinear potential theory
• Partial regularity for minimizers of variational integrals with discontinuous integrands
• Thin sets in nonlinear potential theory
• A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E
• A beginner's guide to the theory of viscosity solutions
• Regularity for degenerate elliptic problems via \(p\)-harmonic approximation
• The \(p\)-harmonic approximation and the regularity of \(p\)-harmonic maps
• Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data
• Linear potentials in nonlinear potential theory
• Riesz potential estimates for a general class of quasilinear equations
• Quasilinear and Hessian equations of Lane-Emden type
• Gradient regularity via rearrangements for \(p\)-Laplacian type elliptic boundary value problems
• The Wolff gradient bound for degenerate parabolic equations
• Riesz potentials and nonlinear parabolic equations
• Universal moduli of continuity for solutions to fully nonlinear elliptic equations
• Global boundedness of the gradient for a class of nonlinear elliptic systems
• The singular set of minima of integral functionals
• Sulla regolarità delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari
• Examples of nonregular solutions of quasilinear elliptic equations with analytic coefficients
• Lorentz estimates for degenerate and singular evolutionary systems
• Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations
• Gradient estimates via non-linear potentials
• Parabolic Systems with Polynomial Growth and Regularity
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Projections onto gradient fields and $L^{p}$-estimates for degenerated elliptic operators
• A note on the Wolff potential estimate for solutions to elliptic equations involving measures
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• On the definition and properties of p-superharmonic functions.
• Hölder gradient estimates for fully nonlinear elliptic equations
• Nonlinear Elliptic Equations with Right Hand Side Measures
• Functions of Vanishing Mean Oscillation
• On the Higher Integrability of the Gradient of Weak Solutions of Certain Degenerate Elliptic Systems
• Weak minima of variational integrals.
• On the weak continuity of elliptic operators and applications to potential theory
• On viscosity solutions of fully nonlinear equations with measurable ingredients
• Uniqueness and maximal regularity for nonlinear elliptic systems of n--Laplace type with measure valued right hand side
• The regularity of general parabolic systems with degenerate diffusion
• Guide to nonlinear potential estimates
• Gradient regularity for nonlinear parabolic equations
• Borderline Estimates for Fully Nonlinear Elliptic Equations
• Non-Lipschitz minimizers of smooth uniformly convex functionals