Note on an eigenvalue problem with applications to a Minkowski type regularity problem in \(\mathbb{R}^n\)

DOI10.1007/s00526-020-1697-7zbMath1445.35180arXiv1906.01576OpenAlexW3006461927MaRDI QIDQ2296685

John L. Lewis, Murat Akman, Andrew L. Vogel

Publication date: 18 February 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.01576

zbMATH Keywords

\(p\)-Laplace equationcone domainsMinkowski regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (2)

A \(L_p\) Brunn-Minkowski theory for logarithmic capacity ⋮ The L_p Minkowski problem for q-capacity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Monge-Ampère equation and its applications
• Carleson type estimates for \(p\)-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces
• Interior a priori estimates for solutions of fully nonlinear equations
• Boundary behavior and the Martin boundary problem for \(p\) harmonic functions in Lipschitz domains
• The spherical \(p\)-harmonic eigenvalue problem in non-smooth domains
• The Brunn-Minkowski inequality and a Minkowski problem for \(\mathcal{A} \)-harmonic Green's function
• The Hadamard variational formula and the Minkowski problem for \(p\)-capacity
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• Separable \(p\)-harmonic functions in a cone and related quasilinear equations on manifolds
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Construction of singular solutions to the p-harmonic equation and its limit equation for \(p=\infty\)
• Regularity for a more general class of quasilinear equations
• A Minkowski problem for electrostatic capacity
• Quasi-linear PDEs and low-dimensional sets
• Global existence for the semigeostrophic equations via Sobolev estimates for Monge-Ampère
• The \(p\)-harmonic measure of small axially symmetric sets
• \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation
• On \(p\)-harmonic measures in half-spaces
• Local behavior of solutions of quasi-linear equations
• Global 𝑊^{2,𝑝} estimates for the Monge-Ampère equation
• Uniform limits of certain A-harmonic functions with applications to quasiregular mappings
• On The Dirichletproblem for Quasilinear Equations
• Boundary regularity for solutions of degenerate elliptic equations
• Some regularity properties of solutions of Monge Ampère equation
• On the regularity of the solution of then-dimensional Minkowski problem
• Geometric properties of the sections of solutions to the Monge-Ampère equation
• The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity
• Note on an eigenvalue problem for an ODE originating from a homogeneous $p$-harmonic function
• Decay of a p-harmonic measure in the plane
• Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains
• The Weyl and Minkowski problems in differential geometry in the large
• The Monge-Ampère equation

This page was built for publication: Note on an eigenvalue problem with applications to a Minkowski type regularity problem in \(\mathbb{R}^n\)