On the analyticity of the semigroups generated by the Hodge-Laplacian, and by the Stokes and Maxwell operators on Lipschitz subdomains of Riemannian manifolds

Marius Mitrea (1) , Sylvie Monniaux (2)

1 Department of Mathematics [New York]
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We study the analyticity of the semigroup generated by the Stokes operator equipped with Neumann-type boundary conditions on Lp spaces in Lipschitz domains. Our strategy is to regularize this operator by considering the Hodge Laplacian, which has the additional property that it commutes with the Leray projection.

Mots clés: Analytic semigroup; Hodge-Laplacian; Lipschitz domains; Analytic semigroup.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]

Marius Mitrea, Sylvie Monniaux. On the analyticity of the semigroups generated by the Hodge-Laplacian, and by the Stokes and Maxwell operators on Lipschitz subdomains of Riemannian manifolds. Transactions of the American Mathematical Society, 2009, 361 (6), pp.3125-3157. ⟨hal-00535701⟩