Garding's Inequality on Manifolds with Boundary

摘要

Garding's inequality for pseudodifferential operators on manifolds with boundary is discussed. The pseudodifferential operators are restricted to operators that are differential in normal direction. Through the technique of symbol smoothing, the main results are shown to hold for symbols with limited smoothness. As an application, general Carleman estimates with boundary terms for elliptic operators as well as for operators with real principal symbols are proved.