Optimal Domain Spaces in Orlicz-sobolev Embeddings
نویسنده
چکیده
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 with respect to a Frostman measure, and, in particular, for trace embeddings on the boundary.
منابع مشابه
Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces
The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega, $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...
متن کاملEntropy Numbers of Trudinger–strichartz Embeddings of Radial Besov Spaces and Applications
The asymptotic behaviour of entropy numbers of Trudinger–Strichartz embeddings of radial Besov spaces on Rn into exponential Orlicz spaces is calculated. Estimates of the entropy numbers as well as estimates of entropy numbers of Sobolev embeddings of radial Besov spaces are applied to spectral theory of certain pseudo-differential operators.
متن کاملRandomized approximation of Sobolev embeddings, II
We study the approximation of Sobolev embeddings by linear randomized algorithms based on function values. Both the source and the target space are Sobolev spaces of non-negative smoothness order, defined on a bounded Lipschitz domain. The optimal order of convergence is determined. We also study the deterministic setting. Using interpolation, we extend the results to other classes of function ...
متن کاملSemicontinuity 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.
متن کاملSeveral Types of Intermediate Besov–orlicz Spaces
The Sobolev spaces have played an essential role in the research of partial differential equations ever since the mid thirties. In order to handle boundary value problems, and, in particular, traces, the more general scales of space have been introduced, namely Slobodeckii spaces and Besov spaces. It proved that Besov spaces are a suitable replacement for Sobolev spaces in many situations and t...
متن کامل