Analysis Seminar

$L^p$ Hardy inequality on $C^{1,\gamma}$ domains

Speaker: Yehuda Pinchover, Technion - Israel Institute of Technology

Location: Warren Weaver Hall 1302

Date: Thursday, February 15, 2018, 11 a.m.

Synopsis:

We consider the $L^p$ Hardy inequality involving the distance to
the boundary of a domain in the $n$-dimensional Euclidean space with
nonempty compact boundary. 

We extend the validity of known existence and non-existence results, as
well as the appropriate tight decay estimates for the corresponding
minimizers, from the case of domains of class $C^2$ to the case of domains
of class $C^{1,\gamma}$ with  $\gamma \in (0,1]$. We consider both bounded
and exterior domains. The upper and lower estimates for the minimizers in the
case of exterior domains and the corresponding related non-existence result
seem to be new even for  $C^2$-domains.

This is joint work with Pier Domenico Lamberti.