@article{LiuWitt2004,
  author    = {Liu, Xiaochun and Witt, Ingo},
  title     = {Pseudodifferential calculi on the half-line respecting prescribed asymptotic types},
  issn      = {0378-620X},
  year      = {2004},
  abstract  = {Given asymptotics types P, Q, pseudodifferential operators A is an element of L-cl(mu) (R+) are constructed in such a way that if u(t) possesses conormal asymptotics of type P as t --> +0, then Au(t) possesses conormal asymptotics of type Q as t --> +0. This is achieved by choosing the operators A in Schulze's cone algebra on the half-line R+, controlling their complete Mellin symbols {sigma(M)(u-j) (A); j is an element of N}, and prescribing the mapping properties of the residual Green operators. The constructions lead to a coordinate invariant calculus, including trace and potential operators at t = 0, in which a parametrix construction for the elliptic elements is possible. Boutet de Monvel's calculus for pseudodifferential boundary problems occurs as a special case when P = Q is the type resulting from Taylor expansion at t = 0.},
  language  = {en}
}
@article{LiuJahnDongetal.2003,
  author    = {Liu, Xiaochun and Jahn, Bor-Ming and Dong, Shuwen and Li, Huimin and Oberh{\"a}nsli, Roland},
  title     = {Neoproterozoic granitoid did not record ultrahigh-pressure metamorphism from the Southern Dabieshan of China},
  issn      = {0022-1376},
  year      = {2003},
  abstract  = {It has been often debated whether all granitic gneisses associated with coesite-bearing eclogites in southern Dabieshan, China, have also been subjected to ultrahigh-pressure (UHP) metamorphism. We show here that a metagranitoid adjacent to the Bixiling eclogite-ultramafic complex has preserved primary granitic textures and an igneous mineral assemblage of biotite + plagioclase + microcline + quartz + allanite +/- amphibole. The absence of UPH recrystallization for the metagranitoid is particularly manifested by the conservation of euhedral-zoned plagioclase phenocrysts, the lack of corona garnets around igneous biotite, and the presence of an igneous mineral assemblage in zircons. The only metamorphic overprint was the epidote-amphibolite facies metamorphism characterized by the assemblage of biotite + phengiticmica + epidote + albite + K-feldspar + quartz +/- amphibole Metamorphic conditions are estimated at ca. 550degrees-680degreesC and 6-13 kbar for the metagranitoid and its amphibolitic enclave. Geochemically, the metagranitoid is similar to its country gneiss and shows an affinity to volcanic arc granitoid. Zircon U-Pb dating suggests that the Bixiling metagranitoid was emplaced during the Neoproterozoic (729+/-4 Ma), when most other granitic rocks and the protoliths of eclogite were also formed in Dabieshan. Taking into account the discovery of non-UHP granitic gneisses in other places, we argue that part of Neoproterozoic granitic rocks in the Dabieshan and Sulu terranes have escaped UHP metamorphism during the Triassic deep subduction of the continental crust as a consequence of a lack of penetrative deformation and fluid-rock interaction},
  language  = {en}
}
@book{LiuWitt2002,
  author    = {Liu, Xiaochun and Witt, Ingo},
  title     = {Pseudodifferential calculi on the half-line respecting prescribed asymptotic types},
  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      = {2002},
  language  = {en}
}
@unpublished{XiaochunWitt2002,
  author    = {Xiaochun, Liu and Witt, Ingo},
  title     = {Pseudodifferential calculi on the half-line respecting prescribed asymptotic types},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26255},
  year      = {2002},
  abstract  = {Contents: 1. Introduction 2. Preliminaries 3. Basic Elements of the Calculus 4. Further Elements of the Calculus},
  language  = {en}
}
@unpublished{XiaochunWitt2001,
  author    = {Xiaochun, Liu and Witt, Ingo},
  title     = {Asymptotic expansions for bounded solutions to semilinear Fuchsian equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25912},
  year      = {2001},
  abstract  = {It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions.},
  language  = {en}
}
@book{LiuWitt2001,
  author    = {Liu, Xiaochun and Witt, Ingo},
  title     = {Asymptotic expansions for bounded solutions to semilinear fuchsian equations},
  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     = {51 S.},
  year      = {2001},
  language  = {en}
}
@unpublished{XiaochunSchulze2004,
  author    = {Xiaochun, Liu and Schulze, Bert-Wolfgang},
  title     = {Boundary value problems in edge representation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26746},
  year      = {2004},
  abstract  = {Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.},
  language  = {en}
}
@article{LiuSchulze2005,
  author    = {Liu, Xiaochun and Schulze, Bert-Wolfgang},
  title     = {Ellipticity on manifolds with edges and boundary},
  issn      = {0026-9255},
  year      = {2005},
  abstract  = {Ellipticity of a manifold with edges and boundary is connected to boundary and edge conditions that complete corresponding operators to Fredholm operators between weighted Sobolev spaces. We study a new parameter-dependent calculus of elliptic operators, where the interior symbols have specific properties on the boundary. We construct elliptic operators with a prescribed number of edge conditions and obtain isomorphisms in the scale of edge Sobolev spaces},
  language  = {en}
}
@book{LiuSchulze2004,
  author    = {Liu, Xiaochun and Schulze, Bert-Wolfgang},
  title     = {Boundary value problems in edge representation},
  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     = {43 S.},
  year      = {2004},
  language  = {en}
}
@book{LiuSchulze2004,
  author    = {Liu, Xiaochun and Schulze, Bert-Wolfgang},
  title     = {Ellipticity on Manifolds with edges and boundary},
  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     = {35 S.},
  year      = {2004},
  language  = {en}
}