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S. Corisco, E. Schrohe & J. Seiler

Differential Operators on Conic Manifolds : Maximal Regularity and Parabolic Equations

(Volume 70 - Année 2001 — Numéro 4 - 5 - 6)
Article
Open Access
Mots-clés : manifolds with conical singularities, quasilinear parabolic equations

Abstract

We study an elliptic differential operator A on a manifold with conic points.  Assuming A to be defined on the smooth functions supported away from the singularities, we first address the question of possible closed extensions of A to Lp Sobolev spaces and then explain how additional ellipticity conditions ensure maximal regularity for the operator A.  Investigating the Lipschitz continuity of the maps f(u) = u, 1, and f(u) = u, N, and using a result of Clément and Li, we finally show unique solvability of a quasilinear equation of the form (t – a(u))u = f(u) in suitable spaces.

1Mathematics Subject Classification : 58J40, 35K65, 47A10

Pour citer cet article

S. Corisco, E. Schrohe & J. Seiler, «Differential Operators on Conic Manifolds : Maximal Regularity and Parabolic Equations», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 70 - Année 2001, Numéro 4 - 5 - 6, 207 – 229 URL : http://popups.ulg.be/0037-9565/index.php?id=1856.

A propos de : S. Corisco

Universita di Torino, Dipartimento di Matematica, V. Carlo Alberto 10, 10123, Torino, Italy, coriasco@dm.unito.it

A propos de : E. Schrohe

Universität Postdam, Institut für Mathematik, Postfach 60 15 53, 14415 Postdam, Germany, schrohe@math.uni-postdam.de

A propos de : J. Seiler

Universität Postdam, Institut für Mathematik, Postfach 60 15 53, 14415 Postdam, Germany, seiler@math.uni-postdam.de