Embedding and compactness theorems for irregular and unbounded domains in weighted Sobolev spaces

Weighted Sobolev spaces and regularity f

Weighted Sobolev spaces and regularity for polyhedral domains

✍ Bernd Ammann; Victor Nistor 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 260 KB

We prove a regularity result for the Poisson problem ÀDu ¼ f , uj oP ¼ g on a polyhedral domain P & R 3 using the Babus ˇka-Kondratiev spaces K m a ðPÞ. These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges [4,33]. In particular, we show that there is no

Embedding of Sobolev space in Orlicz spa

Embedding of Sobolev space in Orlicz space for a domain with irregular boundary

✍ B. V. Trushin 📂 Article 📅 2006 🏛 SP MAIK Nauka/Interperiodica 🌐 English ⚖ 196 KB

Hodge–Helmholtz decompositions of weight

Hodge–Helmholtz decompositions of weighted Sobolev spaces in irregular exterior domains with inhomogeneous and anisotropic media

✍ Dirk Pauly 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 327 KB

## Abstract We study in detail Hodge–Helmholtz decompositions in nonsmooth exterior domains Ω⊂ℝ^__N__^ filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms of rank __q__ belonging to the weighted L^2^‐space L~__s__~^2, __q__^(Ω), __s__∈ℝ, into ir

Trace Theorems for Anisotropic Weighted

Trace Theorems for Anisotropic Weighted SOBOLEV Spaces in a Corner

✍ Bruno Franchi 📂 Article 📅 1986 🏛 John Wiley and Sons 🌐 English ⚖ 969 KB

In this paper, we prove a trace theorem for anisotropic weighted Sobolev spaces in a cube Q naturally associated to a class of degenerate elliptic operators. The fundamental property of this class is the existence of a suitable metric d which is "natural" for the operators. The basic tool of the pro

Trace Theorems for Anisotropic Weighted

Trace Theorems for Anisotropic Weighted SOBOLEV Spaces in a Corner

✍ Bruno Franchi 📂 Article 📅 1986 🏛 John Wiley and Sons 🌐 English ⚖ 969 KB

In this paper, we prove a trace theorem for anisotropic weighted Sobolev spaces in a cube Q naturally associated to a class of degenerate elliptic operators. The fundamental property of this class is the existence of a suitable metric d which is "natural" for the operators. The basic tool of the pro

Local compactness for linear elasticity

Local compactness for linear elasticity in irregular domains

✍ Norbert Weck 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 278 KB

## Abstract For the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector‐valued __L__^2^‐functions whose symmetrized Jacobians are square‐integrable should be compactly embedded in __L__^2^. For regions with the cone property this is usually a