Calculus of Variations and Geometric Measure Theory

G. Psaradakis - D. Spector

A Leray-Trudinger Inequality

created by spector on 30 Jul 2014
modified on 12 Oct 2015


J. Funct. Anal.

Inserted: 30 jul 2014
Last Updated: 12 oct 2015

Pages: 12
Year: 2014


We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case $p=n\geq2.$ 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 $p>n\geq1$ in G. Psaradakis, An optimal Hardy-Morrey inequality, Calc. Var. Partial Differential Equations 45 (3-4) (2012) 421-441.