Viscosity solutions to the infinity Laplacian equation with strong absorptions
type: Item
instance of: scholarly article
title: Viscosity solutions to the infinity Laplacian equation with strong absorptions
zbMATH Open document ID: 1503.35066
author: Yanyan Li
published in: Communications on Pure and Applied Analysis
publication date: 2022-11-23T00:00:00Z
review text: The manuscript under review considers the Dirichlet problem of the inhomogeneous \(\infty\)-Laplace equation of reaction-diffusion type. The authors first prove the existence and uniqueness of the viscosity solution via Perron's method, similar to that in [\textit{G. Lu} and \textit{P. Wang}, Adv. Math. 217, No. 4, 1838--1868 (2008; Zbl 1152.35042)]. Then they study the growth of \(u\) near the free boundary \(\{u>0\}\cap \Omega\) and obtain results similar to those in the homogeneous case [\textit{D. J. Araújo} et al., J. Funct. Anal. 270, No. 6, 2249--2267 (2016; Zbl 1344.35034)].
reviewed by: Yi Ru-Ya Zhang
Mathematics Subject Classification ID: 35D40
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 7622318
zbMATH Keywords: infinity Laplacian
zbMATH Keywords: viscosity solutions
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: regularity
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: cpaa.2022142
OpenAlex ID: W4312502235
cites work: Infinity Laplacian equation with strong absorptions
cites work: Minimization problems for the functional \(\displaystyle{\sup_x}\, F(x,f(x),f'(x))\). I, II
cites work: A tour of the theory of absolutely minimizing functions
cites work: An axiomatic approach to image interpolation
cites work: User’s guide to viscosity solutions of second order partial differential equations
cites work: Reaction-diffusion equations for the infinity Laplacian
cites work: Differential equations methods for the Monge-Kantorovich mass transfer problem
cites work: \(C^{1,\alpha}\) regularity for infinity harmonic functions in two dimensions
cites work: Everywhere differentiability of infinity harmonic functions
cites work: Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
cites work: An asymptotic sharp Sobolev regularity for planar infinity harmonic functions
cites work: Some sharp Sobolev regularity for inhomogeneous infinity Laplace equation in plane
cites work: On the regularity of solutions of the inhomogeneous infinity Laplace equation
cites work: Inhomogeneous infinity Laplace equation
cites work: A PDE Perspective of the Normalized Infinity Laplacian
cites work: Tug-of-war and the infinity Laplacian
cites work: Optimal regularity at the free boundary for the infinity obstacle problem
cites work: Q3777640
cites work: Regularity for the fully nonlinear dead-core problem
DOI: 10.3934/CPAA.2022142
description: scientific article; zbMATH DE number 7622318