Let Ω be a domain in or a noncompact Riemannian manifold of dimension , and . Consider the functional defined on , and assume that . The aim of the paper is to generalize to the quasilinear case () some of the results obtained in [6] for the linear case (), and in particular, to obtain “as large as possible” nonnegative (optimal) Hardy-type weight W satisfying
Our main results deal with the case where , and Ω is a general punctured domain (for we obtain only some partial results). In the case , an optimal Hardy-weight is given by
@article{AIHPC_2016__33_1_93_0, author = {Devyver, Baptiste and Pinchover, Yehuda}, title = {Optimal {\protect\emph{L}} \protect\textsuperscript{ \protect\emph{p} } {Hardy-type} inequalities}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {93--118}, publisher = {Elsevier}, volume = {33}, number = {1}, year = {2016}, doi = {10.1016/j.anihpc.2014.08.005}, mrnumber = {3436428}, zbl = {1331.35013}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2014.08.005/} }
TY - JOUR AU - Devyver, Baptiste AU - Pinchover, Yehuda TI - Optimal L p Hardy-type inequalities JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 93 EP - 118 VL - 33 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2014.08.005/ DO - 10.1016/j.anihpc.2014.08.005 LA - en ID - AIHPC_2016__33_1_93_0 ER -
%0 Journal Article %A Devyver, Baptiste %A Pinchover, Yehuda %T Optimal L p Hardy-type inequalities %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 93-118 %V 33 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2014.08.005/ %R 10.1016/j.anihpc.2014.08.005 %G en %F AIHPC_2016__33_1_93_0
Devyver, Baptiste; Pinchover, Yehuda. Optimal L p Hardy-type inequalities. Annales de l'I.H.P. Analyse non linéaire, Volume 33 (2016) no. 1, pp. 93-118. doi : 10.1016/j.anihpc.2014.08.005. http://www.numdam.org/articles/10.1016/j.anihpc.2014.08.005/
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