Unbounded supersolutions of some quasilinear parabolic equations: A dichotomy. (January 2016)

• Record Type: Journal Article
• Authors: Kinnunen, Juha; Lindqvist, Peter
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 229
• Page End: 242
• Publication Date: 2016-01
• Subjects: primary 35K55 -- secondary 35K65 35K20 31C45; Evolutionary p-Laplace equation -- Viscosity solutions -- Supercaloric functions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.08.016
• Languages: English
• ISSNs: 0362-546X

Abstract

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.