@article{Witt2004, author = {Witt, Ingo}, title = {Local asymptotic types}, issn = {0025-2611}, year = {2004}, abstract = {The local theory of asymptotic types is elaborated. It appears as coordinate-free version of part of GOHBERG- SIGAL'S theory of the inversion of finitely meromorphic, operator-valued functions at a point}, language = {en} } @article{DreherWitt2005, author = {Dreher, M and Witt, Ingo}, title = {Energy estimates for weakly hyperbolic systems of the first order}, year = {2005}, abstract = {For a class of first-order weakly hyperbolic pseudo-differential systems with finite time degeneracy, well- posedness of the Cauchy problem is proved in an adapted scale of Sobolev spaces. These Sobolev spaces are constructed in correspondence to the hyperbolic operator under consideration, making use of ideas from the theory of elliptic boundary value problems on manifolds with singularities. In addition, an upper bound for the loss of regularity that occurs when passing from the Cauchy data to the solutions is established. In many examples, this upper bound turns out to be sharp}, language = {en} } @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{YinWitt2004, author = {Yin, H. C. and Witt, Ingo}, title = {Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data}, issn = {0022-0396}, year = {2004}, abstract = {We study the global singularity structure of solutions to 3-D semilinear wave equations with discontinuous initial data. More precisely, using Strichartz' inequality we show that the solutions stay conormal after nonlinear interaction if the Cauchy data are conormal along a circle. (C) 2003 Elsevier Inc. All rights reserved}, language = {en} } @book{Witt2003, author = {Witt, Ingo}, title = {Green formulae for cone differential operators}, 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 = {25 S.}, year = {2003}, language = {en} } @phdthesis{Witt2003, author = {Witt, Ingo}, title = {Beitr{\"a}ge zur Theorie singul{\"a}rer hyperbolischer Differentialoperatoren}, address = {Potsdam}, pages = {121 S.}, year = {2003}, language = {de} } @book{Witt2002, author = {Witt, Ingo}, title = {A calculus for a class of finitely degenerate pseudodifferential operators}, 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 = {27 S.}, year = {2002}, 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} } @book{Witt2002, author = {Witt, Ingo}, title = {Local 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 = {21 S.}, year = {2002}, language = {en} } @book{YinWitt2002, author = {Yin, Huicheng and Witt, Ingo}, title = {Global singularity structure of weak solutions to 3-D semilinear dispersive wave equaions with discontinuous initial data}, 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 = {13 S.}, year = {2002}, language = {en} }