The existence of extremal functions for discrete Sobolev inequalities on lattice graphs

Abstract

In this paper, we study the existence of extremal functions of the discrete Sobolev inequality and Hardy-Littlewood-Sobolev inequality on lattice graphs. We introduce the discrete Concentration-Compactness principle, and prove the existence of extremal functions for the best constants in the supercritical cases.

16 pages

References in corpus (1)

• Blow-up for a semilinear heat equation with Fujita's critical exponent on locally finite graphs