GAMMA-CONVERGENCE RESULTS FOR PHASE-FIELD APPROXIMATIONS OF THE 2D-EULER ELASTICA FUNCTIONALΓ-convergencerelaxationsingular perturbationgeometric measure theoryWe establish some new results about the Γ-limit, with respect to the L~1-topology, of two different (but related) phase-field approximations {...
Gamma-convergence for Beginners豆瓣评分:0.0 简介:The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematic
Van Gennip, Y., Bertozzi, A. L. Gamma-convergence of graph Ginzburg-Landau functionals. Advances in Differential Equations 17.11/12: 1115-1180 (2012)Van Gennip, Y., Bertozzi, A.L.: Gamma-convergence of graph Ginzburg-Landau functionals. Adv. Differ. Equ. 17(11/12), 1115-1180 (2012)...
Our analysis, which applies $\\Gamma$-convergence techniques, shows that, in an elastic setting, minimizers and the minimal energies of the fully atomistic problem and its related quasicontinuum approximation have the same limiting behaviour as the number of atoms tends to infinity. In case of ...
摘要: We show that the nonlinear bending theory of shells arises as a Gamma-limit of three-dimensional nonlinear elasticity关键词: Theoretical or Mathematical/ bending convergence elasticity shells (structures)/ nonlinear bending theory three-dimensional nonlinear elasticity shells Gamma-convergence/ A0340D...
on a complex line bundle over a closed Riemannian manifold of dimensionn\ge 3. This functional is the natural generalisation of the Ginzburg–Landau model for superconductivity to the non-Euclidean setting. We prove a\Gamma-convergence result, in the strongly repulsive limit, on the functional res...
Gamma-convergenceasymptotic expansionsnext-to-nearest neighbour interactionsfractureIn this work we consider a one-dimensional chain of atoms which interact ... L Scardia,A Schl?Merkemper,C Zanini - 《Mathematical Models & Methods in Applied Sciences》 被引量: 45发表: 2011年 Semi-Dirichlet forms,...
i ned as an ex-ponential version of the inequalities on closed and open sets stated above for the narrowconvergence; and the Brycs-Varadhan theorem [5, Chapter 4.4] can be regarded as a LargeDeviations’ (LD) analog of the characterization of narrow convergence by the convergenceof integrals...
rigorous derivation of elasticity theories for thin structures (often referred to asdimension reduction). (D-C) discrete-to-continuum limits. (F) fracture mechanics. An important tool in all these three branches is-convergence. [19,20]
摘要: Direct methods 15 1 F-convergence by numbers 19 1.1 Some preliminaries 19 1.1.1 Lower 321.7.3 Approximation of lower-semicontinuous functions 33 1.7.4 The direct method .'14 1.8 inLp spares 47 2.4 Problems on Sobolev spaces 50 2.4.1 Weak convergence in Sobolev...