With the advent of sketch-based methods for shape construction, there is a new degree of power availablecreating several models.

Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries uses methods from PDEs, Calculus of Variations, Geometric Measure Theory, and Harmonic Analysis. The most important mathematical challenge in this context is ...

The gradual behaviour of articulatory supralaryangeal variations as a function as an 8-level vs a 4-level prosodic hierarchy was analysed here. Comparisons between the results related to each hierarchy suggested that 4-level hierarchy was sufficient to account for prosodic-dependent articulatory changes in French. These results allowed to discuss the architecture of hierarchical prosodic repres...

We consider nonnegative minimizers of the functional

In this paper we present a result concerning the existence of two nonzero nonnegative solutions for the following Dirichlet problem involving the p -Laplacian ( −∆pu = λf(x, u) in Ω, u = 0 on ∂Ω, using variational methods. In particular, we will determine an explicit real interval Λ for which these solutions exist for every λ ∈ Λ. We also point out that our result improves and extends to higher...

This work contains examples of regular 2D problems of the Calculus of Variations which exhibit stable Lavrentiev phenomenon , under different types of boundary conditions.

In this thesis we study calculus of variations for differential forms. In the first part we develop the framework of direct methods of calculus of variations in the context of minimization problems for functionals of one or several differential forms of the type, ∫

Electrostatically deflected elastic systems are increasingly used in technical applications. We study a typical situation as a free boundary problem and prove, under quite general hypotheses, the existence of a local branch of solutions. Hadamard’s variational formula is crucial in the proof, which is based on the implicit function theorem in Banach spaces. c © 2007 Elsevier Ltd. All rights res...