Schauder estimates for a class of non-local elliptic equations

By Hongjie Dong, Doyoon Kim. 2011

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We prove Schauder estimates for a class of non-local elliptic operators with kernel $K(y)=a(y)/|y|^{d+\sigma}$ and either Dini or Holder continuous data. Here $0 0$. Several local estimates and an extension to operators with kernels $K(x,y)$ are also discussed.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0574a4544e4ddff24b5982e86c80759599c2e85d

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Schauder estimates for solutions of linear parabolic integro-differential equations (2014, background): “, [1, 2, 11, 16] and global Schauder estimates for some linear parabolic nonlocal equations with non-symmetric kernels were obtained in [22] using probabilistic arguments, compared to which a feature of our estimate (1.”
On the Cauchy Problem for Integro-differential Operators in Hölder Classes and the Uniqueness of the Martingale Problem (2011, background): “The elliptic problem Lu = f inRd was considered in [2], [4], [10].”
Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions (2019, result): “These results should be compared with the known C and C local estimates for solutions to inhomogeneous fractional Laplace equations by Silvestre, Caffarelli-Stinga, and other authors ([8, 21, 5, 9]).”
Delaunay-type singular solutions for the fractional Yamabe problem (2015, unknown): “2 from [14] that (−∆)γv ∈ Cα and moreover the following estimate holds: ‖(−∆)v‖Cα ≤ c (‖v‖Cα + ‖f‖Cα) .”
C 1, α Interior Regularity for Nonlinear Nonlocal Elliptic Equations with Rough Kernels (2013, background): “A purely analytic approach is taken in [8], where a local result is proven (see Corollary 1.”