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課程名稱 |
橢圓與拋物方程解的凸性性質
Concavity properties for elliptic and parabolic equations |
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開課學期 |
112-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
石毛和弘 |
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課號 |
MATH5291 |
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課程識別碼 |
221EU9320 |
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班次 |
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學分 |
1.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
第9,10,11,12,13 週
星期二8,9(15:30~17:20)星期四8,9(15:30~17:20) |
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上課地點 |
天數102天數102 |
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備註 |
本課程以英語授課。密集課程。上課時間：10/31-11/27(密集課程)與高田了合授
總人數上限：50人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
In 1976 Brascamp and Lieb proved that the log-concavity is preserved by the Dirichlet heat flow. Their proof is based on the Borell—Brascamp—Lieb (BBL) inequality, which is a generalization of the Prekopa─Leinder (PL) inequality. In this lecture we discuss PL inequality and BBL inequality, and prove the preservation of log-concavity by the heat flow. Additionally, we prove an alternative proof based on the concavity maximum principle and another proof using viscosity solutions. Finally, we discuss the eventual log-concavity by the heat flow. The schedule of the lectures is the following. |
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課程目標 |
We expect students to have basic knowledge in concavity properties toward their future research in geometric analysis of the shape of solutions to PDEs. |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
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參考書目 |
R. J. Gardner, The Brunn-Minkowski inequality, Bull. Amer. Math. Soc. 39 (2002), 355-405. |
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評量方式
(僅供參考) |
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