Abstract
AbstractWe study closed extensions of an elliptic differential operator A on amanifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent exists in a sector of the complex plane and decays like as Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of .As an application we treat the Laplace–Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem , u(0) = 0.
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