On the Hölder regularity for solutions of integro-differential equations like the anisotropic fractional Laplacian

E. B. dos Santos () and R. Leitão ()
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E. B. dos Santos: Universidade Federal do Ceará-UFC
R. Leitão: Universidade Federal do Ceará-UFC

Partial Differential Equations and Applications, 2021, vol. 2, issue 2, 1-34

Abstract: Abstract In this paper we study integro-differential equations like the anisotropic fractional Laplacian. As in Silvestre (Indiana Univ Math J 55:1155–1174, 2006), we adapt the De Giorgi technique to achieve the $$C^{\gamma }$$ C γ -regularity for solutions of class $$C^{2}$$ C 2 and use the geometry found in Caffarelli et al. (Math Ann 360(3–4): 681–714, 2014) to get an ABP estimate, a Harnack inequality and the interior $$C^{1, \gamma }$$ C 1 , γ regularity for viscosity solutions.

Keywords: Fractional Laplacian; Integro-differential equations; Regularity theory; Anisotropy; 26A33; 35J70; 47G20; 35J60; 35D35; 35D40; 35B65 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00083-x

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