Optimal second order boundary regularity for solutions to p-Laplace equations

2023/05/15 by Luigi Montoro, Montoro, Luigi, Luigi Muglia +3 · 3 citations
Mathematics · #35B65 #35J60 #35j25 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2305.08447

openalex publication_date 2023/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Solutions to p-Laplace equations are not, in general, of class C². The study of Sobolev regularity of the second derivatives is, therefore, a crucial issue. An important contribution by Cianchi and Maz'ya shows that, if the source term is in L², then the field |∇ u|^p-2∇ u is in W^1,2. The L²-regularity of the source term is also a necessary condition. Here, under suitable assumptions, we obtain sharp second order estimates, thus proving the optimal regularity of the vector field |∇ u|^p-2∇ u, up to the boundary.

Cited by

• Regularity for a strongly degenerate equation with explicit u-dependence
• Second-order boundary estimates for solutions to a class of quasilinear elliptic equations
• Weak comparison principle for widely degenerate elliptic equations

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