Unbounded supersolutions of some quasilinear parabolic equations: A dichotomy: A dichotomy

Juha Kinnunen, Peter Lindqvist*

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We study unbounded "supersolutions" of the evolutionary p-Laplace equation with slow diffusion. They are the same functions as the viscosity supersolutions. A fascinating dichotomy prevails: either they are locally summable to the power p - 1 + n/p - 0 or not summable to the power p - 2. There is a void gap between these exponents. Those summable to the power p - 2 induce a Radon measure, while those of the other kind do not. We also sketch similar results for the Porous Medium Equation. (C) 2015 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)229-242
Number of pages14
JournalNONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS
Volume131
DOIs
Publication statusPublished - Jan 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Evolutionary p-Laplace equation
  • Viscosity solutions
  • Supercaloric functions
  • HARNACK TYPE INEQUALITIES
  • SEMICONTINUOUS SUPERSOLUTIONS

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