Calculus of Variations and Geometric Measure Theory

A. Braides - A. Malchiodi

Curvature theory of boundary phases: the two-dimensional case

created on 26 May 2001
modified on 05 Dec 2002


Published Paper

Inserted: 26 may 2001
Last Updated: 5 dec 2002

Journal: Interfaces and Free Boundary
Volume: 4
Pages: 345-370
Year: 2002


We describe the behaviour of minimum problems involving non-convex surface integrals in 2D singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted.

Keywords: surface energies, Gamma-convergence $\Gamma$-convergence, phase transitions,, curvature functionals