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Nichtlineare partielle Differentialgleichungen vom gemischten elliptisch-hyperbolischen Typ

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Erstveröffentlichung
2017-08-28
Authors
Bartholomäus, Lukas
Referee
Schulz, Friedmar
Dall'Acqua, Anna
Dissertation


Faculties
Fakultät für Mathematik und Wirtschaftswissenschaften
Institutions
Institut für Analysis
Abstract
This thesis studies the article "Local solutions to a class of Monge-Ampère equations of mixed type" by Qing Han (Duke Math. J., Vol. 136, No. 3, 2007). The article proves the existence of sufficiently smooth local solutions for a special kind of Monge-Ampère equations, which change their type monotonically across a hypersurface from elliptic to hyperbolic resp. vice versa, where the order of degeneracy may be infinite. We elaborate Han's proof via Nash-Moser iterations for solutions of the linearized equations, which are degenerately elliptic resp. hyperbolic, fill some gaps und correct a few inaccuracies.
Date created
2016
Subject headings
[GND]: Monge-Ampère-Differentialgleichung
[LCSH]: Monge-Ampère equations
[Free subject headings]: Nash-Moser Iteration | Monge-Ampère Gleichung | Degeneriert elliptisch | Degeneriert hyperbolisch
[DDC subject group]: DDC 510 / Mathematics
License
Standard
https://oparu.uni-ulm.de/xmlui/license_v3

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DOI & citation

Please use this identifier to cite or link to this item: http://dx.doi.org/10.18725/OPARU-4498

Bartholomäus, Lukas (2017): Nichtlineare partielle Differentialgleichungen vom gemischten elliptisch-hyperbolischen Typ. Open Access Repositorium der Universität Ulm und Technischen Hochschule Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-4498
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