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Search: All articles in the CJM digital archive with keyword Manifolds with conical singularities

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1. CJM 2007 (vol 59 pp. 742)

Gil, Juan B.; Krainer, Thomas; Mendoza, Gerardo A.
 Geometry and Spectra of Closed Extensions of Elliptic Cone Operators We study the geometry of the set of closed extensions of index $0$ of an elliptic differential cone operator and its model operator in connection with the spectra of the extensions, and we give a necessary and sufficient condition for the existence of rays of minimal growth for such operators. Keywords:resolvents, manifolds with conical singularities, spectral theor, boundary value problems, GrassmanniansCategories:58J50, 35J70, 14M15

2. CJM 2005 (vol 57 pp. 771)

Schrohe, E.; Seiler, J.
 The Resolvent of Closed Extensions of Cone Differential Operators We study closed extensions $\underline A$ of an elliptic differential operator $A$ on a manifold with conical singularities, acting as an unbounded operator on a weighted $L_p$-space. Under suitable conditions we show that the resolvent $(\lambda-\underline A)^{-1}$ exists in a sector of the complex plane and decays like $1/|\lambda|$ as $|\lambda|\to\infty$. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of $\underline A$. 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 $\dot{u}-\Delta u=f$, $u(0)=0$. Keywords:Manifolds with conical singularities, resolvent, maximal regularityCategories:35J70, 47A10, 58J40