@book{KapanadzeSchulze2003, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Crack theory and edge singularities}, series = {Mathematics and its applications}, volume = {561}, journal = {Mathematics and its applications}, publisher = {Kluwer Acad. Publ}, address = {Dordrecht}, isbn = {1-4020-1524-0}, pages = {485 S.}, year = {2003}, language = {en} } @book{KapanadzeSchulze2000, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Pseudo-differential Crack Theory}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {62 S.}, year = {2000}, language = {en} } @book{KapanadzeSchulze2000, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary value problems on manifolds with exits to infinity}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {57 S.}, year = {2000}, language = {en} } @book{KapanadzeSchulzeWitt2000, author = {Kapanadze, David and Schulze, Bert-Wolfgang and Witt, Ingo}, title = {Coordinate invarince of the cone algebra with asymptotics}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {42 S.}, year = {2000}, language = {en} } @book{KapanadzeSchulze2001, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Crack theory and edge singularities : Chapter I}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739x}, pages = {IV, 71 S.}, year = {2001}, language = {en} } @book{KapanadzeSchulze2001, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Crack theory and edge singularities : Chapter II}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739x}, pages = {IV, 5 S., S. 72 - 122}, year = {2001}, language = {en} } @book{KapanadzeSchulze2001, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Crack theory and edge singularities : Chapter VI}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739x}, pages = {IV, 5 S., S. 229 - 292}, year = {2001}, language = {en} } @book{KapanadzeSchulze2001, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Crack theory and edge singularities : Chapter V}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739x}, pages = {IV, 5 S., S. 293 - 342}, year = {2001}, language = {en} } @book{KapanadzeSchulze2001, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Crack theory and edge singularities : Chapter III}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739x}, pages = {IV, 5 S., S. 123 - 229}, year = {2001}, language = {en} } @book{KapanadzeSchulze2001, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Symbolic calcullus for boundary value problems on manifolds with edges}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {39 S.}, year = {2001}, language = {en} } @book{KapanadzeSchulze2003, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Asymptotics of potentials in the edge calculus}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {34 S.}, year = {2003}, language = {en} } @book{KapanadzeSchulze2004, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary-contact Problems for Domains with Conical Singularities}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {37 S.}, year = {2004}, language = {en} } @article{KapanadzeSchulze2005, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary-contact problems for domains with conical singularities}, issn = {0022-0396}, year = {2005}, abstract = {We study boundary-contact problems for elliptic equations (and systems) with interfaces that have conical singularities. Such problems represent continuous operators between weighted Sobolev spaces and subspaces with asymptotics. Ellipticity is formulated in terms of extra transmission conditions along the interfaces with a control of the conormal symbolic structure near conical singularities. We show regularity and asymptotics of solutions in weighted spaces, and we construct parametrices. The result will be illustrated by a number of explicit examples. (c) 2004 Elsevier Inc. All rights reserved}, language = {en} } @book{KapanadzeSchulze2005, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary-contact Problems for Domains with Edges Singularities}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1613-3307}, pages = {26 S.}, year = {2005}, language = {en} } @book{KapanadzeSchulzeSeiler2006, author = {Kapanadze, David and Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Operators with singular trace conditions on a manifold with edges}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {33 S.}, year = {2006}, language = {en} } @unpublished{KapanadzeSchulze2005, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary-contact problems for domains with edge singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29901}, year = {2005}, abstract = {We study boundary-contact problems for elliptic equations (and systems) with interfaces that have edge singularities. Such problems represent continuous operators between weighted edge spaces and subspaces with asymptotics. Ellipticity is formulated in terms of a principal symbolic hierarchy, containing interior, transmission, and edge symbols. We construct parametrices, show regularity with asymptotics of solutions in weighted edge spaces and illustrate the results by boundary-contact problems for the Laplacian with jumping coefficients.}, language = {en} } @unpublished{KapanadzeSchulze2003, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Asymptotics of potentials in the edge calculus}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26530}, year = {2003}, abstract = {Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by sbmanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous perators between cone or edge Sobolev spaces and subspaces with asymptotics.}, language = {en} } @unpublished{KapanadzeSchulze2001, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Symbolic calculus for boundary value problems on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26046}, year = {2001}, abstract = {Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy of symbols. The symbol structure is responsible or ellipicity and for the nature of parametrices within an algebra of "edge-degenerate" pseudo-differential operators. The edge symbol component of that hierarchy takes values in boundary value problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in this theory, in particular, the contribution with holomorphic operatot-valued Mellin symbols. We establish a calculus in s framework of "twisted homogenity" that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces. We then derive an equivalent representation with a particularly transparent composition behaviour.}, language = {en} } @unpublished{KapanadzeSchulze2000, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Pseudo-differential crack theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25759}, year = {2000}, abstract = {Crack problems are regarded as elements in a pseudo-differential algbra, where the two sdes int S± of the crack S are treated as interior boundaries and the boundary Y of the crack as an edge singularity. We employ the pseudo-differential calculus of boundary value problems with the transmission property near int S± and the edge pseudo-differential calculus (in a variant with Douglis-Nirenberg orders) to construct parametrices od elliptic crack problems (with extra trace and potential conditions along Y) and to characterise asymptotics of solutions near Y (expressed in the framework of continuous asymptotics). Our operator algebra with boundary and edge symbols contains new weight and order conventions that are necessary also for the more general calculus on manifolds with boundary and edges.}, language = {en} } @unpublished{KapanadzeSchulze2000, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary value problems on manifolds with exits to infinity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25727}, year = {2000}, abstract = {We construct a new calculus of boundary value problems with the transmission property on a non-compact smooth manifold with boundary and conical exits to infinity. The symbols are classical both in covariables and variables. The operators are determined by principal symbol tuples modulo operators of lower orders and weights (such remainders are compact in weighted Sobolev spaces). We develop the concept of ellipticity, construct parametrices within the algebra and obtain the Fredholm property. For the existence of Shapiro-Lopatinskij elliptic boundary conditions to a given elliptic operator we prove an analogue of the Atiyah-Bott condition.}, language = {en} } @unpublished{KapanadzeSchulzeWitt2000, author = {Kapanadze, David and Schulze, Bert-Wolfgang and Witt, Ingo}, title = {Coordinate invariance of the cone algebra with asymptotics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25671}, year = {2000}, abstract = {The cone algebra with discrete asymptotics on a manifold with conical singularities is shown to be invariant under natural coordinate changes, where the symbol structure (i.e., the Fuchsian interior symbol, conormal symbols of all orders) follows a corresponding transformation rule.}, language = {en} }