Differential Operators on Conic Manifolds : Maximal Regularity and Parabolic Equations
Universita di Torino, Dipartimento di Matematica, V. Carlo Alberto 10, 10123, Torino, Italy, coriasco@dm.unito.it
Universität Postdam, Institut für Mathematik, Postfach 60 15 53, 14415 Postdam, Germany, schrohe@math.uni-postdam.de
Universität Postdam, Institut für Mathematik, Postfach 60 15 53, 14415 Postdam, Germany, seiler@math.uni-postdam.de
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