Fractional Sobolev regularity for fully nonlinear elliptic equations

Abstract

Abstract We prove higher-order fractional Sobolev regularity for fully nonlinear, uniformly elliptic equations in the presence of unbounded source terms. More precisely, we show the existence of a universal number depending only on ellipticity constants and dimension, such that if u is a viscosity solution of then, with appropriate estimates. Our strategy suggests a sort of fractional feature of fully nonlinear diffusion processes, as what we actually show is that for a universal constant We believe our techniques are flexible and can be adapted to various models and contexts.