Page 1

Displaying 1 – 10 of 10

Showing per page

Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional

Luca Mugnai (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We establish some new results about the Γ-limit, with respect to the L1-topology, of two different (but related) phase-field approximations { } , { ˜ } ℰ ε ε ,   x10ff65; ℰ ε ε of the so-called Euler’s Elastica Bending Energy for curves in the plane. In particular we characterize theΓ-limit as ε → 0 of ℰε, and show that in general the Γ-limits of ℰεand ˜ x10ff65; ℰ ε do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of theΓ-limit of ˜ x10ff65;...

Structure of stable solutions of a one-dimensional variational problem

Nung Kwan Yip (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...

Currently displaying 1 – 10 of 10

Page 1