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解析学火曜セミナー
過去の記録 ～10/19｜次回の予定｜今後の予定 10/20～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 号室 |
|---|---|
| 担当者 | 石毛 和弘，宮本 安人，坂井 秀隆，三竹 大寿，高田 了 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
今後の予定
2025年10月28日(火)
15:00-17:30 数理科学研究科棟(駒場) 002号室
今回は講演が2件あります。日時・場所にご注意ください。
Lauri Särkiö 氏 (Aalto University) 15:00-16:00
Gradient higher integrability of parabolic double-phase equations (English)
Global well-posedness for 3D quadratic nonlinear Schrödinger equations (Japanese)
今回は講演が2件あります。日時・場所にご注意ください。
Lauri Särkiö 氏 (Aalto University) 15:00-16:00
Gradient higher integrability of parabolic double-phase equations (English)
[ 講演概要 ]
Elliptic double-phase problems have been studied extensively in the last decade since a series of results by Mingione and others. Recently several regularity results have been obtained also for parabolic double-phase equations, yet many questions remain unsolved. In this talk, we focus on gradient higher integrability, showing that solutions to parabolic double-phase equations belong to a slightly higher Sobolev class than assumed a priori. The talk is based on joint work with Wontae Kim, Juha Kinnunen and Kristian Moring.
木下 真也 氏 (名古屋大学) 16:30-17:30Elliptic double-phase problems have been studied extensively in the last decade since a series of results by Mingione and others. Recently several regularity results have been obtained also for parabolic double-phase equations, yet many questions remain unsolved. In this talk, we focus on gradient higher integrability, showing that solutions to parabolic double-phase equations belong to a slightly higher Sobolev class than assumed a priori. The talk is based on joint work with Wontae Kim, Juha Kinnunen and Kristian Moring.
Global well-posedness for 3D quadratic nonlinear Schrödinger equations (Japanese)
[ 講演概要 ]
In this talk, we consider the Cauchy problem of the 3D nonlinear Schrödinger equations. It is known that if the nonlinearity is homogeneous of degree $p >2$, the general theory would provide the small data global existence of 3D NLS. In the quadratic case, which can be seen as a threshold of the small data global existence, the structure of nonlinearity plays a role and more sophisticated analysis is required. The aim in this talk is to show the global well-posedness in the scaling critical space with an additional angular regularity. The proof is based on the Fourier restriction norm method combined with several linear and bilinear estimates for the linear solutions.
In this talk, we consider the Cauchy problem of the 3D nonlinear Schrödinger equations. It is known that if the nonlinearity is homogeneous of degree $p >2$, the general theory would provide the small data global existence of 3D NLS. In the quadratic case, which can be seen as a threshold of the small data global existence, the structure of nonlinearity plays a role and more sophisticated analysis is required. The aim in this talk is to show the global well-posedness in the scaling critical space with an additional angular regularity. The proof is based on the Fourier restriction norm method combined with several linear and bilinear estimates for the linear solutions.
2025年12月09日(火)
16:00-17:30 数理科学研究科棟(駒場) 002号室
Marco Squassina 氏 (Università Cattolica del Sacro Cuore)
Log-concave solutions of the log-Schrodinger equation in a convex domain (English)
Marco Squassina 氏 (Università Cattolica del Sacro Cuore)
Log-concave solutions of the log-Schrodinger equation in a convex domain (English)
[ 講演概要 ]
First, we discuss some recent results on power concavity for certain classes of quasi-linear elliptic problems. We then turn our attention to a new problem involving the so-called log-Schrödinger equation, which cannot be addressed within the standard framework. To handle this, we introduce new techniques that lead to the existence of log-concave solutions to the log-Schrödinger equation in convex domains. Finally, we conclude with a brief discussion of (quantitative) partial concavity results for both elliptic and parabolic problems, as well as some perspectives on future developments concerning (quantitative) quasi-radiality results for problems in the ball.
First, we discuss some recent results on power concavity for certain classes of quasi-linear elliptic problems. We then turn our attention to a new problem involving the so-called log-Schrödinger equation, which cannot be addressed within the standard framework. To handle this, we introduce new techniques that lead to the existence of log-concave solutions to the log-Schrödinger equation in convex domains. Finally, we conclude with a brief discussion of (quantitative) partial concavity results for both elliptic and parabolic problems, as well as some perspectives on future developments concerning (quantitative) quasi-radiality results for problems in the ball.
