Embedding of Orlicz-Sobolev spaces in Hölder 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 ...

Embedding Orlicz Sequence Spaces into C(α)

Let M be a non-degenerate Orlicz function such that there exist ǫ > 0 and 0 < s < 1 with ∑ ∞ i=1 M(ǫs)/M(s) < ∞. It is shown that the Orlicz sequence space hM is isomorphic to a subspace of C(ω). It is also shown that for any non-degenerate Orlicz function M , hM does not embed into C(α) for any α < ω .

Semicontinuity of Vectorial Functionals in Orlicz-sobolev Spaces

We study integral vectorial functionals F(u;) ? Z f(x; u(x); Du(x))dx where f satisses quasi-convexity assumption and its growth is controlled in term of N-functions. We obtain semicontinuity results in the weak * topology of Orlicz-Sobolev spaces.

Some Approximation Properties in Musielak-Orlicz-Sobolev Spaces

Some approximation theorems involving the modular convergence, which improve known density results of interest in the existence theory for strongly nonlinear boundary value problems are presented.

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces