The Mather measure and a Large Deviation Principle for the Entropy Penalized Method
| dc.creator | Gomes, Diogo A. | |
| dc.creator | Lopes, Artur O. | |
| dc.creator | Mohr, Joana | |
| dc.date | 2007-07-17 | |
| dc.date | 2008-11-23 | |
| dc.date.accessioned | 2026-07-07T10:19:52Z | |
| dc.date.available | 2026-07-07T10:19:52Z | |
| dc.description | We present a large deviation principle for the entropy penalized Mather problem when the Lagrangian L is generic (in this case the Mather measure $μ$ is unique and the support of $μ$ is the Aubry set). Consider, for each value of $ε$ and h, the entropy penalized Mather problem $\min \{\int_{\tn\times\rn} L(x,v)dμ(x,v)+εS[μ]\},$ where the entropy S is given by $S[μ]=\int_{\tn\times\rn}μ(x,v)\ln\frac{μ(x,v)}{\int_{\rn}μ(x,w)dw}dxdv,$ and the minimization is performed over the space of probability densities $μ(x,v)$ that satisfy the holonomy constraint It follows from D. Gomes and E. Valdinoci that there exists a minimizing measure $μ_{ε, h}$ which converges to the Mather measure $μ$. We show a LDP $\lim_{ε,h\to0} ε\ln μ_{ε,h}(A),$ where $A\subset \mathbb{T}^N\times\mathbb{R}^N$. The deviation function I is given by $I(x,v)= L(x,v)+\nablaϕ_0(x)(v)-\bar{H}_{0},$ where $ϕ_0$ is the unique viscosity solution for L. | |
| dc.identifier | https://arxiv.org/abs/0707.2603 | |
| dc.identifier | http://arxiv.org/abs/0707.2603 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174665 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 37A50, 37J50 | |
| dc.title | The Mather measure and a Large Deviation Principle for the Entropy Penalized Method | |
| dc.type | text |