GARDING INEQUALITY ON UNBOUNDED DOMAINS

摘要

This note presents a simple method to generalize the Card-ing 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 do-mains (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.