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The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis ofâ€¦ (More)

- Olivier Ley
- 2001

This paper is concerned with rst-order time-dependent Hamilton-Jacobi Equations. Exploiting some ideas of Barron and Jensen 9], we derive lower bound estimates for the gradient of a locally Lipschitzâ€¦ (More)

- Francesca Da Lio, Olivier Ley
- SIAM J. Control and Optimization
- 2006

In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman andâ€¦ (More)

- Guy Barles, Pierre Cardaliaguet, Olivier Ley, RÃ©gis Monneau
- SIAM J. Math. Analysis
- 2008

We are interested in nonlocal Eikonal Equations arising in the study of the dynamics of dislocations lines in crystals. For these nonlocal but also non monotone equations, only the existence andâ€¦ (More)

In this article, we provide existence results for a general class of nonlocal and nonlinear second-order parabolic equations. The main motivation comes from front propagation theory in the cases whenâ€¦ (More)

- Aris Daniilidis, Olivier Ley, STÃ‰PHANE SABOURAU
- 2008

We hereby introduce and study the notion of self-contracted curves, which encompasses orbits of gradient systems of convex and quasiconvex functions. Our main result shows that boundedâ€¦ (More)

- Pierre Cardaliaguet, Olivier Ley, Pierre Cardaliaguetand
- 2008

In [8] we have defined a viscosity solution for the gradient flow of the exterior Bernoulli free boundary problem. We prove here that the associated energy is non decreasing along the flow. Thisâ€¦ (More)

- Pierre Cardaliaguetand, Olivier Ley
- 2007

Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduceâ€¦ (More)

We study the asymptotic behavior of Lipschitz continuous solutions of nonlinear degenerate parabolic equations in the periodic setting. Our results apply to a large class of Hamilton-Jacobi-Bellmanâ€¦ (More)

- Pierre Cardaliaguetand, Olivier Ley

Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduceâ€¦ (More)