Cordes-nirenberg type results for nonlocal equations with deforming kernels.

Abstract. We derive Cordes-Nirenberg type results for nonlocal elliptic equations with deforming kernels using a compactness method.Under a natural integrability assumption for the Monge-Ampere solution, we are able to prove a stability lemma that allows the ellipticity class to vary. As a consequence, we get that the limit equation, up to a rotation, behaves like rough fractional Laplacians where the known regularity theory for this class of  equation can be applied.

Posted on Jun 8, 2023 in Differential Equations, Seminars