@unpublished{SchroheSeiler2002, author = {Schrohe, Elmar and Seiler, J{\"o}rg}, title = {The resolvent of closed extensions of cone differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26378}, year = {2002}, abstract = {We study an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A )-¹ exists in a sector of the complex plane and decays like 1/|λ| as |λ| -> ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with striaght conical degeneracy and establish maximal regularity for the Cauchy problem u - Δu = f, u(0) = 0.}, language = {en} } @unpublished{SchulzeSeiler2002, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Pseudodifferential boundary value problems with global projection conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26233}, year = {2002}, abstract = {Contents: Introduction 1 Operators with the transmission property 1.1 Operators on a manifold with boundary 1.2 Conditions with pseudodifferential projections 1.3 Projections and Fredholm families 2 Boundary value problems not requiring the transmission property 2.1 Interior operators 2.2 Edge amplitude functions 2.3 Boundary value problems 3 Operators with global projection conditions 3.1 Construction for boundary symbols 3.2 Ellipticity of boundary value problems with projection data 3.3 Operators of order zero}, language = {en} }