On the Bakry-Emery criterion for linear diffusions and weighted porous media equations
| dc.creator | Dolbeault, Jean | |
| dc.creator | Nazaret, Bruno | |
| dc.creator | Savaré, Giuseppe | |
| dc.date | 2007-12-13 | |
| dc.date.accessioned | 2026-07-07T08:49:04Z | |
| dc.date.available | 2026-07-07T08:49:04Z | |
| dc.description | The goal of this paper is to give a non-local sufficient condition for generalized Poincaré inequalities, which extends the well-known Bakry-Emery condition. Such generalized Poincaré inequalities have been introduced by W. Beckner in the gaussian case and provide, along the Ornstein-Uhlenbeck flow, the exponential decay of some generalized entropies which interpolate between the $L^2$ norm and the usual entropy. Our criterion improves on results which, for instance, can be deduced from the Bakry-Emery criterion and Holley-Stroock type perturbation results. In a second step, we apply the same strategy to non-linear equations of porous media type. This provides new interpolation inequalities and decay estimates for the solutions of the evolution problem. The criterion is again a non-local condition based on the positivity of the lowest eigenvalue of a Schrödinger operator. In both cases, we relate the Fisher information with its time derivative. Since the resulting criterion is non-local, it is better adapted to potentials with, for instance, a non-quadratic growth at infinity, or to unbounded perturbations of the potential. | |
| dc.identifier | https://arxiv.org/abs/0712.2211 | |
| dc.identifier | http://arxiv.org/abs/0712.2211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144168 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B40; 35K55; 39B62; 35J10; 35K20; 35K65 | |
| dc.title | On the Bakry-Emery criterion for linear diffusions and weighted porous media equations | |
| dc.type | text |