Existence issues for a large class of degenerate elliptic equations with nonlinear Hamiltonians

2020/04/15 by Isabeau Birindelli, Birindelli, I., Giulio Galise +2
Mathematics · #Nonlinear Partial Differential Equations #Geometry and complex manifolds #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2004.07189

Abstract

We give sufficient conditions for the existence and uniqueness, in bounded uniformly convex domains Ω, of solutions of degenerate elliptic equations depending also on the nonlinear gradient term H, in term of the size of Ω, of the forcing term f and of H. The results apply to a wide class of equations, having as principal part significant examples, e.g. linear degenerate operators, weighted partial trace operators and the homogeneous Monge-Ampère operator.

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