Minimum principles and a priori estimates for some translating soliton type problems. (October 2019)

• Record Type: Journal Article
• Authors: Enache, Cristian; López, Rafael
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 352
• Page End: 364
• Publication Date: 2019-10
• Subjects: 35B38 -- 35J93 -- 53A10 -- 35J60; Mean curvature flow -- Translating solitons -- Critical points -- Nodal lines -- Maximum principles -- A priori estimates; 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.2019.05.008
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we are dealing with two classes of mean curvature type problems that generalize the translating soliton problem. A first result proves that the solutions to these problems have unique interior critical points. Using this uniqueness result, we next derive a priori C 0 and C 1 estimates for the solutions to these problems, by means of some minimum principles for appropriate P -functions, in the sense of L. E. Payne.