Differential Operators on Conic Manifolds: Maximal Regularity and Parabolic Equations

الأصل · EN

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, with real α≥ 1, and f(u)=uα, 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.