@article{ChangHedayatMahmoudiSchulze2017, author = {Chang, Der-Chen and Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {Singular degenerate operators}, series = {Applicable analysis : an international journal}, volume = {96}, journal = {Applicable analysis : an international journal}, number = {14}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {0003-6811}, doi = {10.1080/00036811.2017.1336546}, pages = {2434 -- 2456}, year = {2017}, abstract = {We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.}, language = {en} } @article{KhalilSchulze2017, author = {Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Boundary problems on a manifold with edge}, series = {Asian-European Journal of Mathematics}, volume = {10}, journal = {Asian-European Journal of Mathematics}, number = {2}, publisher = {World Scientific}, address = {Singapore}, issn = {1793-5571}, doi = {10.1142/S1793557117500875}, pages = {43}, year = {2017}, abstract = {We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel's theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.}, language = {en} } @article{ChangSchulze2017, author = {Chang, Der-Chen and Schulze, Bert-Wolfgang}, title = {Ellipticity on spaces with higher singularities}, series = {Science China Mathematics}, volume = {60}, journal = {Science China Mathematics}, number = {11}, publisher = {Science China Press}, address = {Beijing}, issn = {1674-7283}, doi = {10.1007/s11425-016-0519-9}, pages = {2053 -- 2076}, year = {2017}, abstract = {We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.}, language = {en} } @article{ChangSchulze2017, author = {Chang, D. -C. and Schulze, Bert-Wolfgang}, title = {Calculus on spaces with higher singularities}, series = {Journal of pseudo-differential operators and applications}, volume = {8}, journal = {Journal of pseudo-differential operators and applications}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-016-0180-x}, pages = {585 -- 622}, year = {2017}, abstract = {We establish extensions of the standard pseudo-differential calculus to specific classes of operators with operator-valued symbols occurring in symbolic hierarchies motivated by manifolds with higher singularities or stratified spaces.}, language = {en} }