On widely degenerate p-Laplace equations with symmetric data

2024/03/17 by Russo, Stefania · 3 citations
#35B65 #35J70 #35J75 #49K20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.11315

Abstract

In this paper, we consider the Dirichlet problems with a widely degenerate equation. Through a well-known result by Talenti, we explicitly express the gradient of the solution u_p outside the ball with a radius of 1, if the datum f is a non-negative radially decreasing function. This allows us to establish some sharp higher regularity results for the weak solutions, assuming that the datum f belongs to a suitable Lorentz space, i.e. under a weaker assumption on the datum with respect to the available literature. Moreover we analyze the behaviour of u_p as p → 1⁺.

Cited by

• Gradient regularity for strongly singular or degenerate elliptic and parabolic equations
• Regularity for a strongly degenerate equation with explicit u-dependence
• Weak comparison principle for widely degenerate elliptic equations

Related

• Regularity for a strongly degenerate equation with explicit u-dependence
• Higher regularity for weak solutions to degenerate parabolic problems
• Lorentz improving estimates for the p-Laplace equations with mixed data
• Gradient bounds for a widely degenerate orthotropic parabolic equation
• Sharp estimates of radial minimizers of p-Laplace equations