Weak comparison principle for widely degenerate elliptic equations

2025/06/27 by Grimaldi, Antonio Giuseppe, Russo, Stefania · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.22128

Abstract

We prove a comparison principle for local weak solutions to a class of widely degenerate elliptic equations of the form -div ( (|Du|-1 )^p-1₊(Du)/(|Du|) ) = f(x,u) in Ω,where p ≥ 2 and Ω is an open subset of ℝⁿ, n≥2. Moreover, we establish some second order regularity results of the solutions, that yields a weighted Sobolev inequality with widely degenerate weights.

Citations

• On widely degenerate p-Laplace equations with symmetric data
• On the second-order regularity of solutions to widely singular or degenerate elliptic equations
• Higher regularity for minimizers of very degenerate convex integrals
• Optimal second order boundary regularity for solutions to p-Laplace equations
• Regularity and symmetry results for nonlinear degenerate elliptic equations
• Hopf Lemma and regularity results for quasilinear anisotropic elliptic equations
• A weak comparison principle for solutions of very degenerate elliptic equations
• Optimal transportation with traffic congestion and Wardrop equilibria

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