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A New Kind of Lax-Oleinik Type Operator with Parameters for Time-Periodic Positive Definite Lagrangian Systems.
- Source :
-
Communications in Mathematical Physics . Feb2012, Vol. 309 Issue 3, p663-691. 29p. - Publication Year :
- 2012
-
Abstract
- In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the family of new Lax-Oleinik type operators with an arbitrary $${u \in C(M, \mathbb{R}^1)}$$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the family of new Lax-Oleinik type operators with an arbitrary $${u \in C(M, \mathbb{R}^1)}$$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 309
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 70383391
- Full Text :
- https://doi.org/10.1007/s00220-011-1375-x