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

Juha Kinnunen; Peter Lindqvist

doi:10.1016/j.na.2015.08.016

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

Juha Kinnunen, Peter Lindqvist^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	229-242
Number of pages	14
Journal	NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS
Volume	131
DOIs	https://doi.org/10.1016/j.na.2015.08.016
Publication status	Published - Jan 2016
MoE publication type	A1 Journal article-refereed

Keywords

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

Access to Document

10.1016/j.na.2015.08.016

http://ac.els-cdn.com/S0362546X15002904/1-s2.0-S0362546X15002904-main.pdf?_tid=03041a0e-ef4f-11e5-9dda-00000aacb362&acdnat=1458556013_fd0db71c7454412b9531b13944e700f8

Cite this

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title = "Unbounded supersolutions of some quasilinear parabolic equations: A dichotomy: A dichotomy",

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.",

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year = "2016",

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doi = "10.1016/j.na.2015.08.016",

language = "English",

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journal = "NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS",

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T2 - A dichotomy

AU - Kinnunen, Juha

AU - Lindqvist, Peter

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AB - 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.

KW - Evolutionary p-Laplace equation

KW - Viscosity solutions

KW - Supercaloric functions

KW - HARNACK TYPE INEQUALITIES

KW - SEMICONTINUOUS SUPERSOLUTIONS

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U2 - 10.1016/j.na.2015.08.016

DO - 10.1016/j.na.2015.08.016

M3 - Article

VL - 131

SP - 229

EP - 242

JO - NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS

JF - NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS

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