Mean value formulas for solutions of some degenerate elliptic equations and applications

HUGO AIMAR, GASTÓN BELTRITTI AND IVANA GÓMEZ

Preprints del IMAL

CONICET-IMAL

Lugar: Santa Fe; Año: 2013 p. 1 - 10

2314-0992

We prove a mean value formula for weak solutions of div(|y|^\alpha grad u) = 0 in R^{n+1} = {(x; y) : x in Rn; y in 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 (-Delta)^s f = 0 on a domain D of Rn. When D is Lipschitz we prove a Besov type regularity improvement for the solutions of (-Delta)^s f = 0.