C1;1-smoothness of constrained solutions in the calculus of variations withapplication to mean field games
| Autor: | Piermarco Cannarsa, Pierre Cardaliaguet, Rossana Capuani |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
021103 operations research Smoothness (probability theory) Applied Mathematics 0211 other engineering and technologies Novelty 02 engineering and technology Construct (python library) State (functional analysis) Lipschitz continuity 020901 industrial engineering & automation Mean field theory Calculus Mathematical Physics Analysis Mathematics |
| Zdroj: | Mathematics in Engineering. 1:174-203 |
| ISSN: | 2640-3501 |
| Popis: | We derive necessary optimality conditions for minimizers of regular functionals in the calculus of variations under smooth state constraints. In the literature, this classical problem is widely investigated. The novelty of our result lies in the fact that the presence of state constraints enters the Euler-Lagrange equations as a local feedback, which allows to derive the C1;1-smoothness of solutions. As an application, we discuss a constrained Mean Field Games problem, for which our optimality conditions allow to construct Lipschitz relaxed solutions, thus improving an existence result due to the first two authors. |
| Databáze: | OpenAIRE |
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