We prove a mean value formula for weak solutions of div(|y| a gradu) = 0 in R n+1 = {(x, y) : x ∈ R n , y ∈ R}, −1 < a < 1, and balls centered at points of the form (x, 0). We obtain an explicit nonlocal kernel for the mean value formula for solutions of (− ) s f = 0 on a domain D of R n . When D is Lipschitz, we prove a Besov type regularity improvement for the solutions of (− ) s f = 0.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.