Differential Operators on Conic Manifolds: Maximal Regularity and Parabolic Equations

2002/01/31 by S. Coriasco, E. Schrohe, J. Seiler · 1 citation
Mathematics · #math.AP #math.FA #msc:58J40 #msc:35K65 #msc:47A10

paper · pdf

published as Bull. Soc. Roy. Sci. Liège 70, fasc. 4-5-6, 207-229 (2001) · 18 pages (revised version, 23/04/'02)

arxiv created 2002/04/23 · arxiv updated 2009/11/30

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 L^p 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|^α, with real α≥ 1, and f(u)=u^α, with αa natural number, and using a result of Clément and Li, we finally show unique solvability of a quasilinear equation of the form u - a(u) Δu = f(u) in suitable spaces.

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• Evolution Equations on Manifolds with Conical Singularities

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