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Tuesday Seminar of Analysis
Seminar information archive ～12/01｜Next seminar｜Future seminars 12/02～
| Date, time & place | Tuesday 16:00 - 17:30 Room # (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | ISHIGE Kazuhiro, MIYAMOTO Yasuhito, SAKAI Hidetaka, MITAKE Hiroyoshi, TAKADA Ryo |
2025/12/09
16:00-17:30 Room # 002 (Graduate School of Math. Sci. Bldg.)
Marco Squassina (Università Cattolica del Sacro Cuore)
Log-concave solutions of the log-Schrodinger equation in a convex domain (English)
Marco Squassina (Università Cattolica del Sacro Cuore)
Log-concave solutions of the log-Schrodinger equation in a convex domain (English)
[ Abstract ]
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.
