Search results for "DOMAIN"
showing 10 items of 2485 documents
On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian
2012
Abstract This paper concerns the best Lipschitz extension problem for a discrete distance that counts the number of steps. We relate this absolutely minimizing Lipschitz extension with a discrete ∞-Laplacian problem, which arises as the dynamic programming formula for the value function of some e -tug-of-war games. As in the classical case, we obtain the absolutely minimizing Lipschitz extension of a datum f by taking the limit as p → ∞ in a nonlocal p -Laplacian problem.
Closedness and lower semicontinuity of positive sesquilinear forms
2009
The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.
Lipschitz operator ideals and the approximation property
2016
[EN] We establish the basics of the theory of Lipschitz operator ideals with the aim of recovering several classes of Lipschitz maps related to absolute summability that have been introduced in the literature in the last years. As an application we extend the notion and main results on the approximation property for Banach spaces to the case of metric spaces. (C) 2015 Elsevier Inc. All rights reserved.
On the regularity of the partial {$O\sp *$}-algebras generated by a closed symmetric operator
1992
Let be given a dense domain D in a Hilbert space and a closed symmetric operator T with domain containing D. Then the restriction of T to D generates (algebraically) two partial *-algebras of closable operators (called weak and strong), possibly nonabelian and nonassociative. We characterize them completely. In particular, we examine under what conditions they are regular, that is, consist of polynomials only, and standard. Simple differential operators provide concrete examples of all the pathologies allowed by the abstract theory.
Quasihyperbolic boundary conditions and Poincaré domains
2002
We prove that a domain in ${\Bbb R}^n$ whose quasihyperbolic metric satisfies a logarithmic growth condition with coefficient $\beta\le 1$ is a (q,p)-\Poincare domain for all p and q satisfying $p\in[1,\infty)\cap(n-n\beta,n)$ and $q\in[p,\beta p^*)$ , where $p^*=np/(n-p)$ denotes the Sobolev conjugate exponent. An elementary example shows that the given ranges for p and q are sharp. The proof makes use of estimates for a variational capacity. When p=2 we give an application to the solvability of the Neumann problem on domains with irregular boundaries. We also discuss the relationship between this growth condition on the quasihyperbolic metric and the s-John condition.
ISOMETRY GROUPS OF WEIGHTED SPACES OF HOLOMORPHIC FUNCTIONS: TRANSITIVITY AND UNIQUENESS
2009
We survey some recent results on the isometries of weighted spaces of holomorphic functions defined on an open subset of ℂn. We will see that these isometries are determined by a subgroup of the automorphisms on a distinguished subset of the domain. We will look for weights with 'large' groups of isometries and observe that in certain circumstances the group of isometries determines the weight.
Geometric Properties of Planar BV -Extension Domains
2009
We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.
General decidability theorems for infinite-state systems
2002
Over the last few years there has been an increasing research effort directed towards the automatic verification of infinite state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems), which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a well-ordered and well-founded preorder such that the transition relation is "monotonic" (is a simulation) with respect to the preorder. We show that the following properties are decidable for …
On the continuity of discrete maximal operators in Sobolev spaces
2014
We investigate the continuity of discrete maximal operators in Sobolev space W 1;p (R n ). A counterexample is given as well as it is shown that the continuity follows under certain sucient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.
Set-valued mappings in partially ordered fuzzy metric spaces
2014
Abstract In this paper, we provide coincidence point and fixed point theorems satisfying an implicit relation, which extends and generalizes the result of Gregori and Sapena, for set-valued mappings in complete partially ordered fuzzy metric spaces. Also we prove a fixed point theorem for set-valued mappings on complete partially ordered fuzzy metric spaces which generalizes results of Mihet and Tirado. MSC:54E40, 54E35, 54H25.