Global estimates for non-symmetric Green type functions with applications to the \(p\)-Laplace equation

DOI10.1007/S11118-008-9095-3zbMath1165.31005OpenAlexW2053270062MaRDI QIDQ956602

Kentaro Hirata

Publication date: 25 November 2008

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-008-9095-3

zbMATH Keywords

quasi-symmetry\(p\)-Green function\(p\)-Martin kernelj\(p\)-harmonic measure

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (11)

Unnamed Item ⋮ TWO-SIDED ESTIMATES FOR POSITIVE SOLUTIONS OF SUPERLINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS ⋮ Existence and nonexistence of a positive solution of the Lane-Emden equation having a boundary singularity: the subcritical case ⋮ Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains ⋮ Boundary estimates for superharmonic functions and solutions of semilinear elliptic equations with source ⋮ The \(p\)-harmonic measure of small axially symmetric sets ⋮ Positive solutions with a time-independent boundary singularity of semilinear heat equations in bounded Lipschitz domains ⋮ On \(p\)-harmonic measures in half-spaces ⋮ Unnamed Item ⋮ A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain ⋮ Phragmén-Lindelöf theorems and \(p\)-harmonic measures for sets near low-dimensional hyperplanes

Cites Work

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• Martin boundary points of a John domain and unions of convex sets
• Boundary Harnack principle for \(p\)-harmonic functions in smooth Euclidean domains
• Singular solutions of the \(p\)-Laplace equation
• Green function for Schrödinger operator and conditioned Feynman-Kac gauge
• Uniform domains and the quasi-hyperbolic metric
• The Green function for uniformly elliptic equations
• Estimates on Green functions and Poisson kernels for symmetric stable processes
• Sharp estimates for the Green function in Lipschitz domains
• Local behavior of solutions of quasi-linear equations
• Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrödinger problems in uniform cones
• Boundary Harnack inequality and a priori estimates of singular solutions of quasilinear elliptic equations
• Isolated singularities of solutions of quasi-linear equations
• Uniform boundary Harnack principle and generalized triangle property
• From Brownian Motion to Schrödinger’s Equation

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