Self-improving properties for a class of elliptic and parabolic equations on bounded domains

We discuss self improving properties of some local and nonlocal, elliptic and parabolic, equations on bounded domains. We employ a functional analytic approach wherein the solution space sits in a suitable interpolation scale. Utilizing a classical analytic perturbation result, we extrapolate the invertibility of the main operator from the base space to nearby spaces within the interpolation family.