Regularity results of nonlinear perturbed stable-like operators

2020/04/15 by Biswas, Anup, Modasiya, Mitesh
#35B65 #45K05 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.06996

Abstract

We consider a class of fully nonlinear integro-differential operators where the nonlocal integral has two components: the non-degenerate one corresponds to the α-stable operator and the second one (possibly degenerate) corresponds to a class of lower order Lévy measures. Such operators do not have a global scaling property. We establish Hölder regularity, Harnack inequality and boundary Harnack property of solutions of these operators.

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