Compact Embeddings Of The Space Of Functions With Bounded Logarithmic Deformation
نویسندگان
چکیده
We introduce the space BLD(Ω) consisting of all fields u : Ω → Rn defined on a domain Ω ⊂ Rn, whose symmetric gradient satisfies ∫ Ω |ε(u)|ln(1 + |ε(u)|) dx < ∞. These fields of bounded logarithmic defomation form a proper subspace of the class BD(Ω) consisting of all functions having bounded deformation. With the help of Reshetnyak’s representation formulas we prove that BLD(Ω) is compactly embedded in Lp(Ω;Rn) even for p = n/n−1. The space BLD(Ω) plays in important role in the theory of plasticity with logarithmic hardening as well as in the modelling of Prandtl-Eyring fluids.
منابع مشابه
Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.
متن کامل-
Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.
متن کاملWeighted composition operators between Lipschitz algebras of complex-valued bounded functions
In this paper, we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators. We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.
متن کاملQuasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...
متن کامل