45 research outputs found
Local behavior of p-harmonic Green's functions in metric spaces
We describe the behavior of p-harmonic Green's functions near a singularity
in metric measure spaces equipped with a doubling measure and supporting a
Poincar\'e inequality
REMOVABLE SETS FOR LIPSCHITZ HARMONIC FUNCTIONS ON CARNOT GROUPS
Abstract. Let G be a Carnot group with homogeneous dimension Q ≥ 3 and let L be a sub-Laplacian on G. We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is (Q − 1). Moreover we construct self-similar sets with positive and finite H Q−1 measure which are removable. 1
Functional Inequalities And Hamilton-Jacobi Equations In Geodesic Spaces
We study the connection between the p-Talagrand inequality and the q-logarithmic Sololev inequality for conjugate exponents p >= 2, q <= 2 in proper geodesic metric spaces. By means of a general Hamilton-Jacobi semigroup we prove that these are equivale