Embeddings of homogeneous Sobolev spaces on the entire space

Affine Embeddings of Homogeneous Spaces

Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneous space G/H admits an affine embedding if and only if G/H is a quasi-affine algebraic variety. We start with some basic properties of affine embeddings and consider the cases, where the theory is well-de...

The Poisson equation in homogeneous Sobolev spaces

We consider Poisson’s equation in an n-dimensional exterior domain G (n≥ 2) with a sufficiently smooth boundary. We prove that for external forces and boundary values given in certain Lq(G)-spaces there exists a solution in the homogeneous Sobolev space S2,q(G), containing functions being local in Lq(G) and having second-order derivatives in Lq(G). Concerning the uniqueness of this solution we ...

On approximation numbers of Sobolev embeddings of weighted function spaces

We investigate asymptotic behaviour of approximation numbers of Sobolev embeddings between weighted function spaces of Sobolev–Hardy–Besov type with polynomials weights. The exact estimates are proved in almost all cases. © 2005 Elsevier Inc. All rights reserved.

Optimal Domain Spaces in Orlicz-sobolev Embeddings

We deal with Orlicz-Sobolev embeddings in open subsets of R. A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible, Orlicz-Sobolev space continuously embedded into a given Orlicz space. Moreover, the optimal Orlicz-Sobolev space is exhibited whenever it exists. Parallel questions are addressed for Orlicz-Sobolev embeddings into Orlicz spaces ...

Optimal Sobolev embeddings and Function Spaces