Existence results for elliptic problems with gradient terms via a priori estimates. (September 2020)

• Record Type: Journal Article
• Authors: Baldelli, Laura; Filippucci, Roberta
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35 J 92 -- 35 J 60; Elliptic problems -- A priori estimates -- Gradient terms; 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.2020.111894
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove existence of nonnegative solutions of a Dirichlet problem on a bounded smooth domain of R N for a p -Laplacian elliptic equation with a convection term. Our proof is based on a priori bounds for a suitable weighted norm involving the distance function from the boundary, obtained by adapting the technique developed by Barrios et al. [4] for nonlocal elliptic problems, which is a modification of the classical scaling blow up method due to Gidas and Spruck in the celebrated paper [25]. The conclusion then follows by using topological degree.