Global boundedness of the gradient for a class of Schrödinger equations. (March 2017)

• Record Type: Journal Article
• Authors: Yang, Sibei
• Is Part Of: Nonlinear analysis. Volume 152(2017)
• Page Start: 102
• Page End: 115
• Publication Date: 2017-03
• Subjects: primary 35J10 -- secondary 35B65 35J25 35D30 35B45; Schrödinger equation -- Dirichlet problem -- Neumann problem -- Boundedness of the gradient -- Uniform exterior ball condition; 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.2017.01.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, via applying the method developed by A. Cianchi and V. Maz'ya, the author obtains the global boundedness of the gradient for solutions to the Dirichlet and the Neumann problems of a class of Schrödinger equations, under the minimal assumptions for the integrability on the data and the regularity on the boundary of the domain. Moreover, the case of arbitrary bounded Lipschitz domains satisfying a uniform exterior ball condition is also considered.