Besov Regularity of Weak solutions to a Class of Nonlinear Elliptic Equations

2024/02/20 by Cheng, Huimin, Zhou, Feng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.12975

Abstract

In this article, we study a Besov regularity estimate of weak solutions to a class of nonlinear elliptic equations in divergence form. The main purpose is to establish Calderon-Zygmund type estimate in Besov spaces with more general assumptions on coefficients, non-homogeneous term and integrable index. By involving the Sharp maximal function, we establish an oscillation estimate of weak solutions in Orlicz-Sobolev spaces. By deriving a higher integrability estimate of weak solutions, we obtain the desired regularity estimate which expands the Calderon-Zygmund theory for nonlinear elliptic equations.

Related

• Regularity results for weak solutions of elliptic PDEs below the natural exponent
• Regularity for fully nonlinear elliptic equations in generalized Orlicz spaces
• Calderón-Zygmund estimates for nonlinear equations of differential forms with BMO coefficients
• Weighted Calderón-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations
• Besov regularity of parabolic and hyperbolic PDEs