Regularity results for a class of doubly nonlinear very singular parabolic equations

Autor:	Vincenzo Vespri, Eurica Henriques, Simona Fornaro
Rok vydání:	2021
Předmět:	010101 applied mathematics Nonlinear system Pure mathematics Class (set theory) Applied Mathematics 010102 general mathematics 0101 mathematics Critical value 01 natural sciences Parabolic partial differential equation Analysis Sign (mathematics) Mathematics
Zdroj:	Nonlinear Analysis. 205:112213
ISSN:	0362-546X
DOI:	10.1016/j.na.2020.112213
Popis:	The aim of this paper is to present several properties of the nonnegative weak solutions to a class of very singular equations whose prototype is u t = div ( u m − 1 | D u | p − 2 D u ) , p > 1 and 3 − p m + p 2 . Namely, we prove L loc r and L loc r − L loc ∞ estimates and Harnack estimates. Note that 3 − p = m + p is a critical value: under this threshold the energy estimates hold with a reverse sign.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5677f8488230dd18bb3f1959311c20ae https://doi.org/10.1016/j.na.2020.112213 Zobrazit plný text záznamu Full Text from ScienceDirect