TY - JOUR

T1 - Differential operators on conic manifolds

T2 - Maximal regularity and parabolic equations

AU - Coriasco, S.

AU - Schrohe, E.

AU - Seiler, J.

N1 - Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2001

Y1 - 2001

N2 - 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|α, α ≥ 1, and f(u) = uα, α ∈ N, and using a result of Clément and Li, we finally show unique solvability of a quasilinear equation of the form (∂t - a(u)Δ)u = f(u) in suitable spaces.

AB - 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|α, α ≥ 1, and f(u) = uα, α ∈ N, and using a result of Clément and Li, we finally show unique solvability of a quasilinear equation of the form (∂t - a(u)Δ)u = f(u) in suitable spaces.

KW - Manifolds with conical singularities

KW - Quasilinear parabolic equations

UR - http://www.scopus.com/inward/record.url?scp=0035738657&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035738657

VL - 70

SP - 207

EP - 229

JO - Bulletin de la Societe Royale des Sciences de Liege

JF - Bulletin de la Societe Royale des Sciences de Liege

SN - 0037-9565

IS - 4-6

ER -