Elliptic methods for solving the linearized field equations of causal variational principles

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...

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Vydáno v:Calculus of variations and partial differential equations Ročník 61; číslo 4
Hlavní autoři: Finster, Felix, Lottner, Magdalena
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022
Springer Nature B.V
Témata:
Analysis
Calculus
Calculus of Variations and Optimal Control; Optimization
Control
Differential calculus
Elliptic functions
Fermions
Function space
Hilbert space
Linearization
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial differential equations
Systems Theory
Theoretical
Variational principles
46E35
49S05
35J50
49Q20
58C35
ISSN:0944-2669, 1432-0835
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-022-02237-0