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

2025/06/29 by Yao Zhang, Xiaofeng Jin, Zhang, Yao +5
Mathematics · #35B45 #35B65 #35R05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.23216

openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the following Dirichlet problem for the fully nonlinear elliptic equation of Grad-Mercier type under asymptotic convexity conditions \ F(D²u(x),Du(x),u(x),x)=g(|\y∈ Ω:u(y)≥ u(x)\|)+f(x) · amp; in Ω, u=ψ · amp;on ∂ Ω. . In order to overcome the non-convexity of the operator F and the nonlocality of the nonhomogeneous term g, we apply the compactness methods and frozen technique to prove the existence of the W^2,p-viscosity solutions and the global W^2,p estimate. As an application, we derive a Cordes-Nirenberg type continuous estimate up to boundary. Furthermore, we establish a global BMO estimate for the second derivatives of solutions by using an asymptotic approach, thereby refining the borderline case of Calderón-Zygmund estimates.

Citations

• Global fractional Sobolev regularity for fully nonlinear elliptic equations
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• Regularity estimates for fully nonlinear elliptic PDEs with general\n Hamiltonian terms and unbounded ingredients
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• On the existence of W²_p solutions for fully nonlinear elliptic equations under either relaxed or no convexity assumptions
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