Gradient regularity for strongly singular or degenerate elliptic and parabolic equations

2025/11/07 by Ambrosio, Pasquale
#35B45 #35B65 #35J70 #35J75 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.05692

Abstract

We present recent advances in the regularity theory for weak solutions to some classes of elliptic and parabolic equations with strongly singular or degenerate structure. The equations under consideration satisfy standard p-growth and p-ellipticity conditions only outside a ball centered at the origin. In the elliptic setting, we describe Besov and Sobolev regularity results for suitable nonlinear functions of the gradient of the weak solutions, covering both the subquadratic (1

Citations

• Gradient regularity for widely degenerate parabolic equations
• Sharp Sobolev regularity for widely degenerate parabolic equations
• 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 weak solutions to degenerate parabolic problems
• Boundary regularity results for minimisers of convex functionals with (p,q)-growth
• Higher differentiability results for solutions to a class of non-homogeneouns elliptic problems under sub-quadratic growth conditions
• The Time Derivative in a Singular Parabolic Equation
• A sharp estimate a la calderon-zygmund for the p--laplacian
• Fractional differentiability for solutions of nonlinear elliptic\n equations
• Hitchhiker's guide to the fractional Sobolev spaces
• On the Time Derivative in an Obstacle Problem
• Parabolic Systems with Polynomial Growth and Regularity

Related

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• Regularity theory for parabolic equations with singular degenerate coefficients
• Sharp Sobolev regularity for widely degenerate parabolic equations
• Regularity for a strongly degenerate equation with explicit u-dependence
• Gradient regularity for widely degenerate elliptic partial differential equations