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

2023/08/22 by Xavier Fernández‐Real, Xavier Ros‐Oton, Fernández-Real, Xavier +1 · 1 citation
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2308.11383

Abstract

We study integro-differential elliptic equations (of order 2s) 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 x, including for the first time operators like ∑_i=1ⁿ(-∂²_vi(x))^s, provided that the coefficients have ``small oscillation''.

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