Optimal Sobolev imbedding spaces

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

A Newton-Imbedding Procedure for Solutions of Semilinear Boundary Value Problems in Sobolev Spaces

This paper is concerned with the application of the Newton-imbedding iteration procedure to nonlinear boundary value problems in Sobolev spaces. A simple model problem for the second-order semilinear elliptic equations is considered to illustrate the main idea. The essence of the method hinges on the a priori estimates of solutions of the associated linear problem in appropriate Sobolev spaces....

Sobolev Spaces

On the Sharpness of the Orlicz - Sobolev Imbedding Theorem ∗

The sharpness of the classical first order Orlicz Sobolev imbedding theorem is discussed in the case in which the Orlicz function increases essentially more slowly than a power function