TY - JOUR
T1 - Unbounded supersolutions of some quasilinear parabolic equations: A dichotomy
T2 - A dichotomy
AU - Kinnunen, Juha
AU - Lindqvist, Peter
PY - 2016/1
Y1 - 2016/1
N2 - 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.
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
UR - http://ac.els-cdn.com/S0362546X15002904/1-s2.0-S0362546X15002904-main.pdf?_tid=03041a0e-ef4f-11e5-9dda-00000aacb362&acdnat=1458556013_fd0db71c7454412b9531b13944e700f8
U2 - 10.1016/j.na.2015.08.016
DO - 10.1016/j.na.2015.08.016
M3 - Article
SN - 0362-546X
VL - 131
SP - 229
EP - 242
JO - NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS
JF - NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS
ER -