| dc.contributor.advisor | Witt, Ingo Prof. Dr. | |
| dc.contributor.author | Spratte, Robin | |
| dc.date.accessioned | 2020-02-24T10:44:10Z | |
| dc.date.available | 2020-02-24T10:44:10Z | |
| dc.date.issued | 2020-02-24 | |
| dc.identifier.uri | http://hdl.handle.net/21.11130/00-1735-0000-0005-1334-B | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-7879 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Paradifferential Operators and Conormal Distributions | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Witt, Ingo Prof. Dr. | |
| dc.date.examination | 2019-10-28 | |
| dc.description.abstracteng | In this thesis we develop a generalization of Hörmander’s symbol calculus of conor-
mal distributions [Hö07, Chapter 18.2] and provide techniques for applications to
nonlinear hyperbolic Partial Differential Equations. In particular we will provide
explicit expansion formulas for symbols of conormal distributions under multiplica-
tion (Theorem 2.16 and Corollary 2.25) and nonlinear superposition with Hölder-
Zygmund continuous functions (Theorem 2.39).
We also define the class of diffeomorphisms of conormal type and establish their
structure as a group (Theorems 2.28 and 2.41), again giving explicit expansion formulas for their symbols. This enables us to define conormal distributions with
respect to non smooth hypersurfaces endowed with the established symbol calculus.
The definitions we give and the methods we develop are applicable to nonlinear
Partial Differential Equations. In Chapter 3 we explicitly construct approximate
symbolic solutions to a Cauchy problem with coefficients and datum given as conormal distributions. We obtain solvability of the reduced problem within a sufficiently
smooth remainder space. In Chapter 4 we provide propagation of conormality for
the developed symbolic calculus under hyperbolic quasilinear equations of first order. | de |
| dc.contributor.coReferee | Bahns, Dorothea Prof. Dr. | |
| dc.subject.eng | PDE | de |
| dc.subject.eng | Nonlinear PDE | de |
| dc.subject.eng | Microlocal Analysis | de |
| dc.subject.eng | Symbol Calculus | de |
| dc.subject.eng | Conormal Distributions | de |
| dc.subject.eng | Paradifferential Operators | de |
| dc.subject.eng | Pseudodifferential Operators | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-21.11130/00-1735-0000-0005-1334-B-5 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.identifier.ppn | 169088956X | |