منابع مشابه
Vector-valued Optimal Lipschitz Extensions
Consider a bounded open set U ⊂ Rn and a Lipschitz function g : ∂U → Rm. Does this function always have a canonical optimal Lipschitz extension to all of U? We propose a notion of optimal Lipschitz extension and address existence and uniqueness in some special cases. In the case n = m = 2, we show that smooth solutions have two phases: in one they are conformal and in the other they are variant...
متن کاملSome Properties of Vector-valued Lipschitz Algebras
Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.
متن کاملOn the character space of vector-valued Lipschitz algebras
We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...
متن کاملOptimal Lipschitz Extensions and the Infinity Laplacian
We reconsider in this paper boundary value problems for the so-called “infinity Laplacian” PDE and the relationships with optimal Lipschitz extensions of the boundary data. We provide some fairly elegant new proofs, which clarify and simplify previous work, and in particular draw attention to the fact that solutions may be characterized by a comparison principle with appropriate cones. We in pa...
متن کاملon the character space of vector-valued lipschitz algebras
we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2011
ISSN: 0010-3640
DOI: 10.1002/cpa.20391