Γ-convergence for Stable States and Local Minimizers

نویسندگان

  • ANDREA BRAIDES
  • CHRISTOPHER J. LARSEN
چکیده

We introduce new definitions of convergence, based on adding stability criteria to Γ-convergence, that are suitable in many cases for studying convergence of local minimizers.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture

Abstract. The energy of the Francfort–Marigo model of brittle fracture can be approximated, in the sense of Γ-convergence, by the Ambrosio–Tortorelli functional. In this work we formulate and analyze two adaptive finite element algorithms for the computation of its (local) minimizers. For each algorithm we combine a Newton-type method with residual-driven adaptive mesh refinement. We present tw...

متن کامل

Slow motion for the nonlocal Allen–Cahn equation in n-dimensions

The goal of this paper is to study the slow motion of solutions of the nonlocal Allen–Cahn equation in a bounded domain Ω ⊂ R, for n > 1. The initial data is assumed to be close to a configuration whose interface separating the states minimizes the surface area (or perimeter); both local and global perimeter minimizers are taken into account. The evolution of interfaces on a time scale ε−1 is d...

متن کامل

Finite Difference Approximation of Free Discontinuity Problems

We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Γ-convergence, and a compactness result which implies, in particular, the convergence of minima and minimizers. AMS (MOS) subject classifications: 49J45, 65K10.

متن کامل

On Multiple Radial Solutions of a Singularly Perturbed Nonlinear Elliptic System

We study radial solutions of a singularly perturbed nonlinear elliptic system of the FitzHughNagumo type. In a particular parameter range, we find a large number of layered solutions. First we show the existence of solutions whose layers are well separated from each other and also separated from the origin and the boundary of the domain. Some of these solutions are local minimizers of a related...

متن کامل

Phase Transitions and Minimal Hypersurfaces in Hyperbolic Space

The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for entire local minimizers with prescribed behaviour at infinity. Then, we study the limit as the length scale tends to zero through a Γ-convergence analysis, obta...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009