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Documents  49Q05 | enregistrements trouvés : 2

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The talk will review the motivations, state of the art, recent results, and open questions on four very related PDE models related to phase transitions: Allen-Cahn, Peierls-Nabarro, Minimal surfaces, and Nonlocal Minimal surfaces. We will focus on the study of stable solutions (critical points of the corresponding energy functionals with nonnegative second variation). We will discuss new nonlocal results on stable phase transitions, explaining why the stability assumption gives stronger information in presence of nonlocal interactions. We will also comment on the open problems and obstructions in trying to make the nonlocal estimates robust as the long-range (or nonlocal) interactions become short-range (or local).
The talk will review the motivations, state of the art, recent results, and open questions on four very related PDE models related to phase transitions: Allen-Cahn, Peierls-Nabarro, Minimal surfaces, and Nonlocal Minimal surfaces. We will focus on the study of stable solutions (critical points of the corresponding energy functionals with nonnegative second variation). We will discuss new nonlocal results on stable phase transitions, explaining ...

82B26 ; 49Q05 ; 53A10 ; 35B35 ; 35R11

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Multi angle  Parametrizing with Guy
Toro, Tatiana (Auteur de la Conférence) | CIRM (Editeur )

Over the past 20 years we have been interested in finding good parameterizations for sets that are well approximated by nice sets. In this talk we will discuss the meanings of good and nice. We will recall some the results from the past and present new results concerning the regularity of sets that can be well approximated by Lipschitz graphs.

28A75 ; 49Q05 ; 49Q20 ; 49Kxx

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