Existence of a weak solution to the p-Sobolev flow. (October 2018)

• Record Type: Journal Article
• Authors: Nakamura, Kenta; Misawa, Masashi
• Is Part Of: Nonlinear analysis. Volume 175(2018)
• Page Start: 157
• Page End: 172
• Publication Date: 2018-10
• Subjects: p-Sobolev flow -- Yamabe flow -- Galerkin method; 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.2018.05.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study a doubly nonlinear parabolic equation, called the p -Sobolev flow here, which is the classical Yamabe flow on a bounded domain in Euclidean space in the case p = 2 . We show the existence of a weak solution to the p -Sobolev flow without geometric assumptions.