Finite speed propagation for parabolic quasiminimizers. (September 2020)

• Record Type: Journal Article
• Authors: Fujishima, Y.; Habermann, J.
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35K55 -- 35B65 -- 49N60; Parabolic quasiminimizers -- Propagation speed -- Degenerate parabolic p-Laplace; 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.2020.111891
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with the propagation speed for parabolic quasiminimizers. More precisely, we show that parabolic quasiminimizers for the p -energy with p > 2 propagate with finite speed. Since parabolic quasiminimizers are in some respects generalizations of solutions to parabolic equations, the results at hand show that the fundamental property of finite speed propagation for solutions of the degenerate parabolic p -Laplace equation ( p > 2 ) are preserved by passing to quasiminimizers.