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Variational principles and free-boundary problems
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The article was published on 1982-01-01 and is currently open access. It has received 1214 citations till now. The article focuses on the topics: Free boundary problem & Obstacle problem.read more
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The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
TL;DR: In this paper, the equivalence between the compactness of all minimizing sequences and some strict sub-additivity conditions was shown based on a compactness lemma obtained with the help of the notion of concentration function of a measure.
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A geometric model for active contours in image processing
TL;DR: A new model for active contours based on a geometric partial differential equation that satisfies the maximum principle and permits a rigorous mathematical analysis is proposed, which enables us to extract smooth shapes and it can be adapted to find several contours simultaneously.
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An analysis of a phase field model of a free boundary
TL;DR: In this paper, a mathematical analysis of a new approach to solidification problems is presented, where a free boundary arising from a phase transition is assumed to have finite thickness, and the physics leads to a system of nonlinear parabolic differential equations.
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Variational problems with two phases and their free boundaries
TL;DR: In this article, the problem of minimizing J{v] = f(Vu|2 + q2(x)X2(v))dx, vGK, where q 2 ¥= 0, (a22 ifu>0, and X 2 u is lower semicontinuous at v = 0, was studied.