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Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011, Article ID 917201, 21 pages doi:10.1155/2011/917201 Research Article Sharp Nonexistence Results for a Linear Elliptic Inequality Involving Hardy and Leray Potentials Mouhamed Moustapha Fall1 and Roberta Musina2 1 Institut fur Mathematik Goethe-Universit¨ t Frankfurt, Robert-Mayer-Straße 10, a ¨ 60054 Frankfurt, Germany 2 Dipartimento di Matematica ed Informatica, Universit` di Udine, via delle Scienze, a 206-33100 Udine, Italy Correspondence should be addressed to Roberta Musina, musina@uniud.it Received 4 January 2011; Accepted 4 March 2011 Academic Editor: Marta Garc´a-Huidobro ı Copyright q 2011 M. M. Fall and R. Musina. This is an open access article distributed. | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 917201 21 pages doi 10.1155 2011 917201 Research Article Sharp Nonexistence Results for a Linear Elliptic Inequality Involving Hardy and Leray Potentials Mouhamed Moustapha Fall1 and Roberta Musina2 1 Institutfur Mathematik Goethe-Universitat Frankfurt Robert-Mayer-Strafie 10 60054 Frankfurt Germany 2 Dipartimento di Matematica ed Informatica Universita di Udine via delle Scienze 206-33100 Udine Italy Correspondence should be addressed to Roberta Musina musina@uniud.it Received 4 January 2011 Accepted 4 March 2011 Academic Editor Marta Garcia-Huidobro Copyright 2011 M. M. Fall and R. Musina. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We deal with nonnegative distributional supersolutions for a class of linear elliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results. 1. Introduction In recent years a great deal work has been made to find necessary and sufficient conditions for the existence of distributional solutions to linear elliptic equations with singular weights. Most of the papers deal with weak solutions belonging to suitable Sobolev spaces. We quote for instance 1-4 and references therein. In the present paper we focus our attention on a class of model elliptic inequalities involving singular weights and we adopt the weakest possible concept of solution that is that one of distributional solution. Let N 2 be an integer R e 0 1 and let BR be the ball in RN of radius R centered at 0. In the first part of the paper we study nonnegative solutions to N- 2 2 -Au-------4---- x 2u a x 2 log x u in D BR 0 1.1 2 Journal of Inequalities and Applications where a R is a varying parameter. By a standard definition a solution to 1.1 is a function u L Br 0
