MATEMATIČKI VESNIK МАТЕМАТИЧКИ ВЕСНИК

 SOME FUNCTION SPACES AND THEIR APPLICATIONS TO ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS N. K. Tumalun, D. I. Hakim, H. Gunawan AbstractIn 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 Pages:  1$-$16

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