A Leray-Trudinger Inequality
Abstract
We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case p=n≥2. In this paper we provide an optimal Sobolev-type improvement of this substitute, analogous to the corresponding improvements obtained for p=2<n in S. Filippas, A. Tertikas, Optimizing improved Hardy inequalities, J. Funct. Anal. 192 (1) (2002) 186--233, and for p>n≥1 in G. Psaradakis, An optimal Hardy-Morrey inequality, Calc. Var. Partial Differential Equations 45 (3-4) (2012) 421--441.
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