Cone Conditions and Properties of Sobolev Spaces

  title={Cone Conditions and Properties of Sobolev Spaces},
  author={John Fournier},
Many of the most common and useful properties of Sobolev spaces defined over a domain (open set) in Euclidean space require that the domain has a minimal degree of regularity. To this end, the domain is often assumed to satisfy a “cone condition.” For example, various imbeddings of Sobolev spaces into Lebesgue spaces or spaces of bounded continuous functions (the Sobolev imbedding theorem), and various interpolation inequalities such as those estimating D-norms of intermediate-order derivatives… CONTINUE READING