Existence results for elliptic problems with gradient terms via a priori estimates. (September 2020) - Baldelli, Laura; Filippucci, Roberta
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.