On the viscosity solutions to some nonlinear elliptic equations

2015/03/16 by Tilak Bhattacharya, Bhattacharya, Tilak, Leonardo Marazzi +1
Computer Science · Mathematics · #35J60 #35J70 #35P30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1503.04879

openalex publication_date 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many instances, show the existence of a first eigenvalue and a first positive eigenfunction.

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