Global weighted Lorentz estimates of oblique tangential derivative problems for weakly convex fully nonlinear operators

2023/02/17 by Junior da S. Bessa, Gleydson C. Ricarte, Bessa, Junior da S. +1 · 1 citation
Mathematics · #Differential Equations and Boundary Problems #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.09177

Abstract

In this work, we develop weighted Lorentz-Sobolev estimates for viscosity solutions of fully nonlinear elliptic equations with oblique boundary condition under weakened convexity conditions in the following configuration F(D²u, Du, u, x) = f(x) in Ω and β⋅ Du+γu=g on ∂ Ω, where Ω is a bounded domain in ℝⁿ (n ≥ 2), under suitable assumptions on the source term f, data β, γ and g. In addition, we obtain Lorentz-Sobolev estimates for solutions to the obstacle problem and others applications.

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

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