Higher differentiability results for solutions to a class of non-homogeneouns elliptic problems under sub-quadratic growth conditions

2022/03/23 by Albert Clop, Clop, Albert, Andrea Gentile +3 · 4 citations
Computer Science · Mathematics · #35J47 #35J70 #49N60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2203.12283

openalex publication_date 2022/03/23 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We prove a sharp higher differentiability result for local minimizers of functionals of the form F(w,Ω)=∫_Ω[ F(x,Dw(x))-f(x)⋅ w(x)]dx with non-autonomous integrand F(x,ξ) which is convex with respect to the gradient variable, under p-growth conditions, with 1

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• Fractional higher differentiability of solutions to strongly nonlinear Stokes systems
• Gradient regularity for strongly singular or degenerate elliptic and parabolic equations
• Regularity for a strongly degenerate equation with explicit u-dependence
• Higher differentiability for solutions to stationary p-Stokes systems under sub-quadratic growth conditions

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