This book deals with a class of mathematical problems which involve the minimization of the
sum of a volume and a surface energy and have lately been refered to as' free discontinuity …

Imaging is an interdisciplinary research area with profound applications in many areas of
science, engineering, technology, and medicine. The most primitive form of imaging is visual …

In this paper it is shown that, under mild continuity and growth hypotheses, if f(x,u,.) is quasi-
convex and if u_n, u∈W^1,1 are such that u_n→u in L^1, then \int_Ωf(x,u(x),∇u(x))dx\leqq …

In this paper it is shown that if f (x, u,.) is a quasiconvex function with linear growth then the
relaxed functional in u-> ff (x, u (x), Vu (x» dx with respect to the L1 topology has an integral …

On the Relaxation in BV(f2; R”) of Quasi-convex Integrals I nf(5+V’P(~))dx~f(5)meas(a) Page 1
JOURNAL OF FUNCTIONAL ANALYSIS 109, 7697 (1992) On the Relaxation in BV(f2; R”) of …

∫ϵ^-1(1-|∇u|^2)^2+ϵ|∇∇u|^2 in two space dimensions. We introduce a new scheme for
proving lower bounds and show the bounds are asymptotically sharp for certain domains …

Anisotropic singular perturbations—the vectorial case Page 1 Proceedings of the Royal Society
of Edinburgh, 124A, 527-571,1994 Anisotropic singular perturbations—the vectorial case Ana …

In this paper we present a new formulation of a large class of phase-field models, which
describe solidification of a pure material and allow for both surface energy and interface …

NOTICE WARNING CONCERNING COPYRIGHT RESTRICTIONS: The copyright law of the
United States (title 17, US Code) governs the makin Page 1 NOTICE WARNING CONCERNING …

A free boundary problem arising from materials science is studied in the one-dimensional
case. The problem studied here is an obstacle problem for the non-convex energy …