Sobolev embeddings and distance functions
Sobolev embeddings and distance functions
Abstract On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi mathvariant="script">D</m:mi> <m:mn>0</m:mn> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> </m:math> \mathcal{D}^{{1,p}}_{0} into <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>L</m:mi> <m:mi>q</m:mi> </m:msup> </m:math> L^{q} and the summability properties of …