The Resolvent of Closed Extensions of Cone Differential Operators

[摘要] We study closed extensions $underline A$ ofan elliptic differential operator $A$ on a manifold with conicalsingularities, acting as an unbounded operator on a weighted $L_p$-space.Under suitable conditions we show that the resolvent $(lambda-underline A)^{-1}$ existsin a sector of the complex plane and decays like $1/|lambda|$ as$|lambda|oinfty$. Moreover, we determine the structure of the resolventwith enough precision to guarantee existence and boundedness of imaginarypowers of $underline A$. As an application we treat the Laplace--Beltrami operator for a metric withstraight conical degeneracy and describe domains yieldingmaximal regularity for the Cauchy problem $dot{u}-Delta u=f$, $u(0)=0$.

[学科分类] 数学（综合）