A Cauchy problem for the Cauchy-Riemann operator
- We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.
Author details: | Ibrahim LyGND |
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DOI: | https://doi.org/10.1007/s13370-020-00810-4 |
ISSN: | 1012-9405 |
ISSN: | 2190-7668 |
Title of parent work (English): | Afrika Matematika |
Publisher: | Springer |
Place of publishing: | Heidelberg |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/07/10 |
Publication year: | 2020 |
Release date: | 2022/11/30 |
Tag: | Cauchy problem; Zaremba problem; nonlinear PDI |
Volume: | 32 |
Issue: | 1-2 |
Number of pages: | 8 |
First page: | 69 |
Last Page: | 76 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |