نتایج جستجو برای: γ بوتیرولاکتون

تعداد نتایج: 74952  

2007
ROBERT L. JERRARD

It is well-known that Γ-convergence of functionals provides a tool for studying global and local minimizers. Here we present a general result establishing the existence of critical points of a Γ-converging sequence of functionals provided the associated Γ-limit possesses a nondegenerate critical point, subject to certain mild additional hypotheses. We then go on to prove a theorem that describe...

2009
Yves van Gennip Mark A. Peletier

Abstract. We study the H-norm of the function 1 on tubular neighbourhoods of curves in R. We take the limit of small thickness ε, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit ε → 0, containing contributions from the length of the curve (at order ε), the ends (ε), and the curvature (ε). The second result is a Γ-convergence r...

2011
OVIDIU SAVIN ENRICO VALDINOCI

We discuss the Γ-convergence, under the appropriate scaling, of the energy functional ‖u‖Hs(Ω) + ∫ Ω W (u) dx, with s ∈ (0, 1), where ‖u‖Hs(Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential. When s ∈ [1/2, 1), we show that the energy Γ-converges to the classical minimal surface functional – while, when s ∈ (0, 1/2), it is easy to see that the functio...

Journal: :SIAM J. Math. Analysis 2016
Roberto Alicandro Maria Stella Gelli

We study, through a Γ-convergence procedure, the discrete to continuum limit of Ising type energies of the form Fε(u) = − ∑ i,j ci,juiuj , where u is a spin variable defined on a portion of a cubic lattice εZ ∩ Ω, Ω being a regular bounded open set, and valued in {−1, 1}. If the constants ci,j are non negative and satisfies suitable coercivity and decay assumptions, we show that all possible Γ-...

2007
G. Alberti S. Baldo G. Orlandi

The distributional k-dimensional Jacobian of a map u in the Sobolev space W 1,k−1 which takes values in the the sphere S can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary M o...

2012
NADIA ANSINI

We study the asymptotic behavior of a sequence of Dirichlet problems for second order linear operators in divergence form { −div(σε∇u) = f in Ω, u ∈ H1 0 (Ω), where (σε) ⊂ L∞(Ω;Rn×n) is uniformly elliptic and possibly non-symmetric. On account of the variational principle of Cherkaev and Gibiansky [1], we are able to prove a variational characterization of the H-convergence of (σε) in terms of ...

2014
Brahim Amaziane Leonid Pankratov

We review recent results on the homogenization in Sobolev spaces with variable exponents. In particular, we are dealing with the Γ-convergence of variational functionals with rapidly oscillating coefficients, the homogenization of the Dirichlet and Neumann variational problems in strongly perforated domains, as well as double porosity type problems.The growth functions also depend on the small ...

2015
Markus Grasmair Monika Muszkieta Otmar Scherzer

In this paper, we present a method for the numerical minimization of the Mumford–Shah functional that is based on the idea of topological asymptotic expansions. The basic idea is to cover the expected edge set with balls of radius ε > 0 and use the number of balls, multiplied with 2ε, as an estimate for the length of the edge set. We introduce a functional based on this idea and prove that it c...

Journal: :Math. Program. 2014
Guy Bouchitté Ilaria Fragalà Ilaria Lucardesi

For ⌦ varying among open bounded sets in Rn with a Lipschitz boundary @⌦, we consider shape functionals J(⌦) defined as the infimum over a Sobolev space of an integral energy of the kind R ⌦[f(ru) + g(u)], under Dirichlet or Neumann conditions on @⌦. Under fairly weak assumptions on the integrands f and g, we prove that, when a given domain ⌦ is deformed into a one-parameter family of domains ⌦...

2017
Luigi De Pascale Jean Louet Filippo Santambrogio

We investigate the approximation of the Monge problem (minimizing ∫ Ω |T (x)− x|dμ(x) among the vector-valued maps T with prescribed image measure T#μ) by adding a vanishing Dirichlet energy, namely ε ∫ Ω |DT |. We study the Γ-convergence as ε → 0, proving a density result for Sobolev (or Lipschitz) transport maps in the class of transport plans. In a certain two-dimensional framework that we a...

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