Bernoulli Variational Problem and Beyond |
| |
Authors: | Alexander Lorz Peter Markowich Benoît Perthame |
| |
Institution: | 1. CNRS UMR 7598, Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06, 4, pl. Jussieu F75252, Paris Cedex 05, France 2. INRIA-Rocquencourt, EPI BANG, Paris, France 3. CSMSE Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
|
| |
Abstract: | The question of ‘cutting the tail’ of the solution of an elliptic equation arises naturally in several contexts and leads to a singular perturbation problem under the form of a strong cut-off. We consider both the PDE with a drift and the symmetric case where a variational problem can be stated. It is known that, in both cases, the same critical scale arises for the size of the singular perturbation. More interesting is that in both cases another critical parameter (of order one) arises that decides when the limiting behaviour is non-degenerate. We study both theoretically and numerically the values of this critical parameter and, in the symmetric case, ask if the variational solution leads to the same value as for the maximal solution of the PDE. Finally we propose a weak formulation of the limiting Bernoulli problem which incorporates both Dirichlet and Neumann boundary condition. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|