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Differential Operators on Conic Manifolds: Maximal Regularity and Parabolic Equations

S. Coriasco·E. Schrohe·J. Seiler
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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\ge 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 \dot{u} - a(u) Δu = f(u) in suitable spaces.

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S. Coriasco, E. Schrohe, J. Seiler. 2002-04-23. Differential Operators on Conic Manifolds: Maximal Regularity and Parabolic Equations. https://arxiv.org/abs/math/0201184

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