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Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations

Francesca Da Lio, Boyan Sirakov (2007)

Journal of the European Mathematical Society

We study uniformly elliptic fully nonlinear equations F ( D 2 u , D u , u , x ) = 0 , and prove results of Gidas–Ni–Nirenberg type for positive viscosity solutions of such equations. We show that symmetries of the equation and the domain are reflected by the solution, both in bounded and unbounded domains.

Symplectic torus actions with coisotropic principal orbits

Johannes Jisse Duistermaat, Alvaro Pelayo (2007)

Annales de l’institut Fourier

In this paper we completely classify symplectic actions of a torus T on a compact connected symplectic manifold ( M , σ ) when some, hence every, principal orbit is a coisotropic submanifold of ( M , σ ) . That is, we construct an explicit model, defined in terms of certain invariants, of the manifold, the torus action and the symplectic form. The invariants are invariants of the topology of the manifold, of the torus action, or of the symplectic form.In order to deal with symplectic actions which are not Hamiltonian,...

Système d'Euler incompressible et régularité microlocale analytique

Pascal Gamblin (1994)

Annales de l'institut Fourier

Dans cet article on étudie la régularité analytique (ou Gevrey) des courbes intégrales de champs de vecteurs solutions non nécessairement lipschitziennes du système d’Euler incompressible. On en déduit que le front d’onde analytique (ou Gevrey) de ces solutions est localisé dans la variété caractéristique de l’opérateur linéarisé.

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