Global fractional Sobolev regularity for fully nonlinear elliptic equations

2024/11/22 by Claudemir Alcantara, Alcantara, Claudemir, Makson S. Santos +1 · 1 citation
Engineering · Mathematics · #35B65 #35J15 #35J25 #35J60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2411.15311

openalex publication_date 2024/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We investigate fractional regularity estimates up to the boundary for solutions to fully nonlinear elliptic equations with measurable ingredients. Specifically, under the assumption of uniform ellipticity of the operator, we demonstrate that viscosity solutions to a second-order operator satisfy a fractional Laplacian equation. This result implies that the solutions are globally of class W^{γ, p}, for γ∈ (1,2), with appropriate estimates. Consequently, these solutions exhibit differentiability of order strictly greater than one, without requiring any additional assumptions regarding the operator, such as convexity or concavity.

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• Global Calderón-Zygmund estimates for asymptotically convex fully nonlinear Grad-Mercier type equations

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