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Laplace type operators: Dirichlet problem

Wojciech Kozł (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We investigate Laplace type operators in the Euclidean space. We give a purely algebraic proof of the theorem on existence and uniqueness (in the space of polynomial forms) of the Dirichlet boundary problem for a Laplace type operator and give a method of determining the exact solution to that problem. Moreover, we give a decomposition of the kernel of a Laplace type operator into 𝖲𝖮 ( n ) -irreducible subspaces.

Large time behaviour of heat kernels on non-compact manifolds: fast and slow decays

Thierry Coulhon (1998)

Journées équations aux dérivées partielles

In this talk we shall present some joint work with A. Grigory’an. Upper and lower estimates on the rate of decay of the heat kernel on a complete non-compact riemannian manifold have recently been obtained in terms of the geometry at infinity of the manifold, more precisely in terms of a kind of L 2 isoperimetric profile. The main point is to connect the decay of the L 1 - L ∞ norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods. We shall...

Le problème d’équivalence locale pour un système scalaire complet d’équations aux dérivées partielles d’ordre deux à n variables indépendantes

Camille Bièche (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Dans le présent article, nous établissons une caractérisation des systèmes scalaires d’équations aux dérivées partielles analytiques d’ordre deux à n variables indépendantes équivalents par un changement de coordonnées analytique au système u x α x β = 0 , 1 ≤ α , β ≤ n .

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