Finster, Felix and Lottner, Magdalena (2022) Elliptic methods for solving the linearized field equations of causal variational principles. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 61 (4): 133. ISSN 0944-2669, 1432-0835
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The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator which is shown to be bounded and symmetric on a Hilbert space endowed with a suitably adapted weighted L-2-scalar product. Guided by the procedure in the theory of linear elliptic partial differential equations, we use the spectral calculus to define Sobolev-type Hilbert spaces and invert the linearized field operator as an operator between such function spaces. The uniqueness of the resulting weak solutions is analyzed. Our constructions are illustrated in simple explicit examples. The connection to the causal action principle for static causal fermion systems is explained.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 07:01 |
| Last Modified: | 07 Feb 2024 07:01 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56584 |
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