Abstract

In this paper we prove Fefferman's inequalities associated to potentials belonging to 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 equation with 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 space or a Stummel class which does not satisfy the strong unique continuation is presented.

Keywords: Morrey spaces; Stummel classes; Fefferman's inequality; srong unique continuation property.

MSC: 26D10, 46E30, 35J15

DOI: 10.57016/MV-cdyn1783

Pages:  71$-$86     

Volume  75 ,  Issue  2 ,  2023