Folk theorems on elliptic equations

Abstract

This chapter reviews folk theorems applicable for elliptic equations. Folk theorems are almost impossible to locate in the literature; although, specialists will always realize that they have known them all the time. These theorems are not deep, and it is very natural that specialists should concentrate their efforts on more important problems. Nevertheless, it may interest some non-specialists to see how the recent progress in the theory of partial differential equations yields, very easily, properties of elliptic operators, which, in classical books, are invariably restricted to operators of the second order. The chapter describes the Gårding-Višik theorem on self-adjoint elliptic operators on a bounded open set in Rn, which is one such folk theorem.