Schauder and Cordes–Nirenberg estimates for nonlocal elliptic equations with singular kernels

2024/08/20 by Xavier Fernández‐Real, Xavier Ros‐Oton
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.1112/plms.12629

Abstract

Abstract We study integro‐differential elliptic equations (of order ) with variable coefficients, and prove the natural and most general Schauder‐type estimates that can hold in this setting, both in divergence and non–divergence form. Furthermore, we also establish Hölder estimates for general elliptic equations with no regularity assumption on , including for the first‐time operators like , provided that the coefficients have “small oscillation.”

Citations

• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• Nonlocal Continuum Field Theories

Related

• Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels
• Nonuniformly elliptic Schauder theory
• Interior Schauder estimates for fractional elliptic equations in nondivergence form
• Hölder and Harnack estimates for integro-differential operators with kernels of measure
• Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders