Search results for "Continuity"
showing 10 items of 378 documents
METRIC DIFFERENTIABILITY OF LIPSCHITZ MAPS
2013
AbstractAn extension of Rademacher’s theorem is proved for Lipschitz mappings between Banach spaces without the Radon–Nikodým property.
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
2020
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti-Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.
Critical points for nondifferentiable functions in presence of splitting
2006
A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. © 2005 Elsevier Inc. All rights reserved.
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
2010
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.
Mappings of finite distortion: The sharp modulus of continuity
2003
We establish an essentially sharp modulus of continuity for mappings of subexponentially integrable distortion.
Mean curvature flow of graphs in warped products
2012
Let M be a complete Riemannian manifold which either is compact or has a pole, and let φ be a positive smooth function on M . In the warped product M ×φ R, we study the flow by the mean curvature of a locally Lipschitz continuous graph on M and prove that the flow exists for all time and that the evolving hypersurface is C∞ for t > 0 and is a graph for all t. Moreover, under certain conditions, the flow has a well defined limit.
Heterogeneous structures studied by an interphase elasto-plastic damaging model
2013
Heterogeneous materials present a mechanical response strongly dependent on the static and kinematic phenomena occurring in the constituents and at their joints. At the mesoscopic level the interaction between the units is simulated by mean of apposite mechanical devices such as the zero thickness interface model where contact tractions and displacement discontinuities are the primary static and kinematic variables respectively. In heterogeneous materials the response also depends on joint internal stresses. The introduction of internal stresses brings to the interphase model or an enhancement of the classical zero-thickness interface. With the term 'interphase' we shall mean a layer separa…
Middleware for transparent TCP connection migration : masking faulty TCP-based services
2004
Masteroppgave i informasjons- og kommunikasjonsteknologi 2004 - Høgskolen i Agder, Grimstad Mission critical TCP-based services create a demand for robust and fault tolerant TCP communication. Sense Intellifield monitors drill operations on rig sites offshore. Critical TCP-based services need to be available 24 hours, 7 days a week, and the service providers need to tolerate server failure. How to make TCP robust and fault tolerant without modifying existing infrastructure like existing client/server applications, services, TCP stacks, kernels, or operating systems is the motivation of this thesis. We present a new middleware approach, first of its kind, to allow TCP-based services to survi…
MR2524292 (2010f:26007): Kolyada, V. I.; Lind, M. On functions of bounded p-variation. J. Math. Anal. Appl. 356 (2009), no. 2, 582–604. (Reviewer: Lu…
2009
For p∈(1,+∞), let f∈Lp be a 1-periodic function on the real line, with the norm of f given by ∥f∥p=(∫10|f(x)|pdx)1/p. The Lp-modulus of continuity of f is defined by ω(f,δ)p=sup0≤h≤δ(∫10|f(x+h)−f(x)|pdx)1/p, 0≤δ≤1. A partition of period 1 (or simply a partition) is a set Π={x0,x1,…,xn} of points such that x0<x1<…<xn=x0+1. For a given partition Π={x0,x1,…,xn} let vp(f;Π)=(∑k=0n−1|f(xk+1)−f(xk)|p)1/p. The modulus of p-continuity of f is defined by ω1−1/p(f,δ)=sup∥Π∥≤δvp(f;Π), where the supremum is taken over all partitions Π such that ∥Π∥=maxk(xk+1−xk)≤δ. In this paper, improving a previous estimate given by A. P. Terehin [Mat. Zametki 2 (1967), 289--300; MR0223512 (36 #6560)], it is shown th…
A Positive Definite Advection Scheme for Use in Long Range Transport Models: Extension to Monotonicity
1992
Numerical modeling of atmospheric transport processes requires the solution of the continuity equation for prognostic variables such as momentum, heat, water vapor, liquid water or chemical species of the atmosphere. Although in the literature many advection schemes are known to solve this problem (Lax and Wendroff 1964, Crowley 1968, Tremback et al. 1987, Bott 1989a,b), these algorithms show different disadvantages, which sometimes yield undesirably poor numerical results. For instance, the upstream method is known to produce large numerical diffusion. The higher order versions of the advection schemes of Tremback et al. (1987) are much less diffusive. Unfortunately, the schemes are not po…