Regularity and Separation for $p$-Laplace operators

Fuente: arXiv
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Main Authors: Hauer, Daniel, Sikora, Adam
Format: Preprint
Published: 2024
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_version_ 1866929221848268800
author Hauer, Daniel
Sikora, Adam
author_facet Hauer, Daniel
Sikora, Adam
contents We analyze $p$-Laplace operators with degenerate elliptic coefficients. This investigation includes Grušin type $p$-Laplace operators. We describe a \emph{separation phenomenon} in elliptic and parabolic $p$-Laplace type equations, which provides an illuminating illustration of simple jump discontinuities of the corresponding weak solutions. Interestingly validity of an isoperimetric inequality for considered setting does not imply continuity of elliptic equations. On the other hand, we are able to establish global $L^1$-$L^\infty$-regularization and decay estimates of every mild solution of the parabolic Grušin type $p$-Laplace equation.
format Preprint
id arxiv_https___arxiv_org_abs_2401_13381
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Regularity and Separation for $p$-Laplace operators
Hauer, Daniel
Sikora, Adam
Analysis of PDEs
58J35, 47H06, 47H20, 47H06, 35J92
We analyze $p$-Laplace operators with degenerate elliptic coefficients. This investigation includes Grušin type $p$-Laplace operators. We describe a \emph{separation phenomenon} in elliptic and parabolic $p$-Laplace type equations, which provides an illuminating illustration of simple jump discontinuities of the corresponding weak solutions. Interestingly validity of an isoperimetric inequality for considered setting does not imply continuity of elliptic equations. On the other hand, we are able to establish global $L^1$-$L^\infty$-regularization and decay estimates of every mild solution of the parabolic Grušin type $p$-Laplace equation.
title Regularity and Separation for $p$-Laplace operators
topic Analysis of PDEs
58J35, 47H06, 47H20, 47H06, 35J92
url https://arxiv.org/abs/2401.13381