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解析学火曜セミナー
過去の記録 ～10/28｜次回の予定｜今後の予定 10/29～
| 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/ |
次回の予定
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.
