Weighted Orlicz regularity for fully nonlinear elliptic equations with oblique derivative at the boundary via asymptotic operators

2023/05/19 by Junior da S. Bessa, Bessa, Junior da S. · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2305.11861

openalex publication_date 2023/05/19 · openalex created_date 2023/05/23 · openalex updated_date 2026/08/01

Abstract

We prove weighted Orlicz-Sobolev regularity for fully nonlinear elliptic equations with oblique boundary condition under asymptotic conditions of the following problem: F(D²u,Du,u,x)=f(x) in the bounded domain Ω⊂ ℝⁿ(n≥ 2) and β⋅ Du+γu= g on ∂ Ω, under suitable assumptions on the source term f, data β, γ and g. Our approach guarantees such estimates under conditions where the governing operator F does not require a convex (or concave) structure. We also deal with weighted Orlicz-type estimates for the obstacle problem with oblique derivative condition on the boundary. As a final application, the developed methods provide weighted Orlicz-BMO regularity for the Hessian, provided that the source lies in that space and in weighted Orlicz space associated.

Cited by

• Weighted Orlicz-Sobolev and variable exponent Morrey regularity for fully nonlinear parabolic PDEs with oblique boundary conditions and applications

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