Wolff potential estimates for elliptic equations with nonstandard growth and applications

DOI10.1515/FORUM.2010.057zbMath1203.35099WikidataQ110086564 ScholiaQ110086564MaRDI QIDQ3060228

Niko Marola, Teemu Lukkari, Fumi-Yuki Maeda

Publication date: 1 December 2010

Published in: Forum Mathematicum (Search for Journal in Brave)

zbMATH Keywords

superharmonic functionselliptic equationsHedberg-Wolff theoremWolff type potential

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items

Extremal solutions of \(p\)-Laplacian problems in \(D^{1, p}(\mathbb{R}^N)\) via Wolff potential estimates, The boundary Harnack inequality for variable exponent \(p\)-Laplacian, Carleson estimates, barrier functions and \(p(\cdot)\)-harmonic measures, Decay estimates for Wolff potentials in \(\mathbb{R}^N\) and gradient-dependent quasilinear elliptic equations, Riesz potential estimates for a class of double phase problems, Nonlinear potential estimates for generalized Stokes system, Wolff potentials and measure data vectorial problems with Orlicz growth, Wolff potential estimates for supersolutions of equations with generalized Orlicz growth, The strong minimum principle for quasisuperminimizers of non-standard growth, Nonlinear measure data problems, Wolff type potential estimates and application to nonlinear equations with negative exponents, Radial symmetry for a weighted integral equation of Wolff type, Overview of differential equations with non-standard growth, Boundary continuity of solutions to elliptic equations with nonstandard growth, Global gradient estimates for a borderline case of double phase problems with measure data, Weak-type estimates and potential estimates for elliptic equations with drift terms, Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

Cites Work

• Unnamed Item
• A-superharmonic functions and supersolutions of degenerate elliptic equations
• A transmission problem in the calculus of variations
• The Wiener test and potential estimates for quasilinear elliptic equations
• Wolff potential estimates of superminimizers of Orlicz type Dirichlet integrals
• Potential estimates for a class of fully nonlinear elliptic equations.
• An obstacle problem and superharmonic functions with nonstandard growth
• Non-linear potentials and approximation in the mean by analytic functions
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• On the definition and properties of p-superharmonic functions.
• Weighted Nonlinear Potential Theory
• A class of De Giorgi type and Hölder continuity
• On the weak continuity of elliptic operators and applications to potential theory
• Gradient estimates for thep(x)-Laplacean system
• Regularity results for a class of functionals with non-standard growth