L^∞-bounds for general singular elliptic equations with convection term

2019/12/19 by Greta Marino, Patrick Winkert, Marino, Greta +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1912.09541

openalex publication_date 2019/12/19 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

In this note we present L^∞-results for problems of the form A(x,u,Du)=B(x,u,Du) in Ω, u>0 in Ω, u=0 on ∂Ω, where the growth condition for the function B\colon Ω× ℝ× ℝ^N→ ℝ contains both a singular and a convection term. We use ideas from the works of Giacomoni-Schindler-Takac (2007) and the authors (2019) to prove the boundedness of weak solutions for such general problem by applying appropriate bootstrap arguments.

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