Search results for "Rearrangement inequality"
showing 2 items of 2 documents
Hardy’s inequality and the boundary size
2002
We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.
On improved fractional Sobolev–Poincaré inequalities
2016
We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a ‘separation property’, is a John domain.