Open Access
Optimal shape design
A. Kwiatkowska,J. Sikora,A. Krawczyk +2 more
- pp 39-51
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The article was published on 1999-01-01 and is currently open access. It has received 60 citations till now. The article focuses on the topics: Shape optimization.read more
Citations
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Journal ArticleDOI
A model for the quasi-static growth of a brittle fracture: existence and approximation results
Gianni Dal Maso,Rodica Toader +1 more
TL;DR: In this article, a variational model for the irreversible quasi-static evolution of a brittle fracture was proposed based on Griffith's theory of crack growth, and the total energy is an absolute continuous function of time, although the bulk energy and surface energy may present some jump discontinuities.
Book
Implicit partial differential equations
TL;DR: In this paper, the authors compare first and second order PDE's with viscosity solutions, and give some preliminary results existence theorems for systems of partial differential equations, including singular values case.
Journal ArticleDOI
Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
Luis A. Caffarelli,Fanghua Lin +1 more
TL;DR: In this paper, the asymptotic limits of solutions of singularly perturbed elliptic systems were studied and uniform Lipschitz regularity and free interfaces between supports of various components of the maps were established.
Journal ArticleDOI
Multi-phase structural optimization via a level set method ∗, ∗∗
TL;DR: It turns out that the optimization of a diffuse interface has its own interest in material science, for example to optimize functionally graded materials and various approaches based on Hadamard method of boundary variations are discussed.
Posted Content
Nodal domains and spectral minimal partitions
TL;DR: In this article, the existence and regularity of the minimal partitions associated with the nodal sets as nodal domains of Courant-sharp eigenfunctions are analyzed. But the main results concern the existence of the nodals and the regularities of minimal partitions.
References
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Book
Implicit partial differential equations
TL;DR: In this paper, the authors compare first and second order PDE's with viscosity solutions, and give some preliminary results existence theorems for systems of partial differential equations, including singular values case.
Journal ArticleDOI
Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
Luis A. Caffarelli,Fanghua Lin +1 more
TL;DR: In this paper, the asymptotic limits of solutions of singularly perturbed elliptic systems were studied and uniform Lipschitz regularity and free interfaces between supports of various components of the maps were established.
Journal ArticleDOI
Nodal Domains and Spectral Minimal Partitions
TL;DR: In this paper, the authors consider two-dimensional Schrodinger operators in bounded domains and analyze relations between the nodal domains of eigenfunctions, spectral minimal partitions and spectral properties of the corresponding operator.
Journal ArticleDOI
Multi-phase structural optimization via a level set method ∗, ∗∗
TL;DR: It turns out that the optimization of a diffuse interface has its own interest in material science, for example to optimize functionally graded materials and various approaches based on Hadamard method of boundary variations are discussed.
Book ChapterDOI
Minimization problems for eigenvalues of the Laplacian
TL;DR: In this article, a survey on minimization problems concerning the lower eigenvalues of the Laplace operator is presented, including the minimization of the second eigenvalue among plane convex domains.