SOME FUNCTION SPACES AND THEIR APPLICATIONS TO ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

Abstract

In this paper we prove Fefferman's inequalities associated to potentials belongingto a generalized Morrey space or a Stummel class.We also show that the logarithm of a non-negative weak solution to a second order elliptic partial differential equationwith potential in a generalized Morrey space or a Stummel class, under some assumptions, belongs to the bounded mean oscillation class.As a consequence, this elliptic partial differential equation has the strong unique continuation property.An example of an elliptic partial differential equation with potential in a Morrey spaceor a Stummel class which does not satisfy the strong unique continuation is presented.