本文印刷
全画面プリント
談話会・数理科学講演会
過去の記録 ～03/27｜次回の予定｜今後の予定 03/28～
| 担当者 | 会田茂樹，大島芳樹，志甫淳（委員長），高田了 |
|---|---|
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index.html |
2024年07月26日(金)
15:30-16:30 数理科学研究科棟(駒場) 大講義室(auditorium)号室
万一感染クラスター発生時にご連絡差し上げるため、[参考URL]から参加登録をお願いいたします。
Juan Manfredi 氏 (University of Pittsburgh)
Mean value expansions for solutions to general elliptic and parabolic equations (English)
https://docs.google.com/forms/d/e/1FAIpQLSefp31yMulPlAUURVHuQK9p41IadOj9KN0l-dD-mpbapJ0K6w/viewform?usp=pp_url
万一感染クラスター発生時にご連絡差し上げるため、[参考URL]から参加登録をお願いいたします。
Juan Manfredi 氏 (University of Pittsburgh)
Mean value expansions for solutions to general elliptic and parabolic equations (English)
[ 講演概要 ]
Harmonic functions in Euclidean space are characterized by the mean value property and are also obtained as expectations of stopped Brownian motion processes. This equivalence has a long history with fundamental contributions by Doob, Hunt, Ito, Kakutani, Kolmogorov, L ́evy, and many others. In this lecture, I will present ways to extend this characterization to solutions of non-linear elliptic and parabolic equations.
The non-linearity of the equation requires that the rigid mean value property be replaced by asymptotic mean value expansions and the Brownian motion by stochastic games, but the main equivalence remains when formulated with the help of the theory of viscosity solutions. Moreover, this local equivalence also holds on more general ambient spaces like Riemannian manifolds and the Heisenberg group.
I will present examples related the Monge-Amp`ere and k-Hessian equations and to the p-Laplacian in Euclidean space and the Heisenberg group.
[ 参考URL ]Harmonic functions in Euclidean space are characterized by the mean value property and are also obtained as expectations of stopped Brownian motion processes. This equivalence has a long history with fundamental contributions by Doob, Hunt, Ito, Kakutani, Kolmogorov, L ́evy, and many others. In this lecture, I will present ways to extend this characterization to solutions of non-linear elliptic and parabolic equations.
The non-linearity of the equation requires that the rigid mean value property be replaced by asymptotic mean value expansions and the Brownian motion by stochastic games, but the main equivalence remains when formulated with the help of the theory of viscosity solutions. Moreover, this local equivalence also holds on more general ambient spaces like Riemannian manifolds and the Heisenberg group.
I will present examples related the Monge-Amp`ere and k-Hessian equations and to the p-Laplacian in Euclidean space and the Heisenberg group.
https://docs.google.com/forms/d/e/1FAIpQLSefp31yMulPlAUURVHuQK9p41IadOj9KN0l-dD-mpbapJ0K6w/viewform?usp=pp_url
