Regularity of solutions for degenerate or singular fully nonlinear integro-differential equations

Source abstract

We study a series of regularity results for solutions to a degenerate or singular fully nonlinear integro-differential equation of the form [Formula: see text] In the degenerate case, we establish borderline regularity, provided the inverse of the degeneracy law [Formula: see text] is Dini-continuous. In addition, we show Schauder-type higher regularity at local extremum points for a specific non-local degenerate equation. In the singular case, we establish Hölder continuity of the gradient for solutions to a general non-local equation. It is noteworthy that these results are new even in the case [Formula: see text]. Finally, as a byproduct of the borderline regularity analysis, we demonstrate how our methods can be applied to study of the corresponding regularity for a class of degenerate non-local normalized p-Laplacian equations.