Please use this identifier to cite or link to this item:
doi:10.22028/D291-40762
Title: | A small remark on Bernstein’s theorem |
Author(s): | Bildhauer, Michael Farquhar, Bernhard Fuchs, Martin |
Language: | English |
Title: | Archiv der Mathematik |
Volume: | 121 |
Issue: | 4 |
Pages: | 437-447 |
Publisher/Platform: | Springer Nature |
Year of Publication: | 2023 |
Free key words: | Bernstein’s theorem Non-parametric minimal surfaces Twodimensional variational problems Splitting-type functionals |
DDC notations: | 510 Mathematics |
Publikation type: | Journal Article |
Abstract: | We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler– Lagrange equation, we receive a result analogous to Bernstein’s theorem on non-parametric minimal surfaces. Without assumptions of this type, Bernstein’s theorem cannot be carried over to the splitting case, which follows from an elementary counterexample. We also include some modifications of our main theorem. |
DOI of the first publication: | 10.1007/s00013-023-01908-4 |
URL of the first publication: | https://doi.org/10.1007/s00013-023-01908-4 |
Link to this record: | urn:nbn:de:bsz:291--ds-407622 hdl:20.500.11880/36634 http://dx.doi.org/10.22028/D291-40762 |
ISSN: | 1420-8938 0003-889X |
Date of registration: | 19-Oct-2023 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Professorship: | MI - Prof. Dr. Martin Fuchs |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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