Garding inequality on unbounded domains

Abstract

This note presents a simple method to generalize the Garding inequality to unbounded domains. By introducing a special partition of unity associated to some covering of unbounded domains, we show that the Garding inequality, known in the literature on bounded domains (see Garding, 1953), holds for more general domains. The method proposed here only requires weak smoothness assumptions which allows coverage of a large class of elliptic operators. It also gives a new tool to extend some local properties to global ones, in particular when we deal with functions vanishing on the boundary.