Bernard, Yann and Finster, Felix (2012) On the structure of minimizers of causal variational principles in the non-compact and equivariant settings. Preprintreihe der Fakultät Mathematik 11/2012, Working Paper.
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:||Monograph (Working Paper)|
|Institutions:||Mathematics > Prof. Dr. Felix Finster|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||22 May 2012 08:40|
|Last Modified:||22 May 2012 08:40|