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 |
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Pages (from-to) | 229-242 |
Number of pages | 14 |
Journal | NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS |
Volume | 131 |
DOIs | |
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