Bernard, Yann and Finster, Felix (2014) On the structure of minimizers of causal variational principles in the non-compact and equivariant settings. ADVANCES IN CALCULUS OF VARIATIONS, 7 (1). pp. 27-57. ISSN 1864-8258, 1864-8266
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We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is supported on the intersection of a hyperplane with a level set of a function which is homogeneous of degree two. Moreover, we perform second variations to obtain that the compact operator representing the quadratic part of the action is positive semi-definite. The key ingredient for the proof is a subtle adaptation of the Lagrange multiplier method to variational principles on convex sets.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Nonconvex variational principles; variational problems with constraints; Lagrange multiplier method on convex sets |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 Nov 2019 14:05 |
| Last Modified: | 29 Nov 2019 14:05 |
| URI: | https://pred.uni-regensburg.de/id/eprint/11098 |
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