| 研究課題/領域番号 |
20K22315
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| 研究種目 |
研究活動スタート支援
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| 配分区分 | 基金 |
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| 審査区分 |
0201:代数学、幾何学、解析学、応用数学およびその関連分野
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| 研究機関 | 沖縄科学技術大学院大学 |
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研究代表者 |
ZHOU Xiaodan 沖縄科学技術大学院大学, 距離空間上の解析ユニット, 准教授 (10871494)
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| 研究期間 (年度) |
2020-09-11 – 2024-03-31
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| 研究課題ステータス |
完了 (2023年度)
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| 配分額 *注記 |
2,860千円 (直接経費: 2,200千円、間接経費: 660千円)
2021年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
2020年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
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| キーワード | eikonal equation / metric measure spaces / viscosity solution / discontinuous data / Heisenberg group / h-quasiconvex functions / metric measure space / h-quasiconvexity / Hamilton-Jacobi equation / differential games / viscosity solutions / metric spaces / HJ equations / well-posedness |
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| 研究開始時の研究の概要 |
Motivated by the rapid developments of optimal transport, control theory, data sciences etc., there is a growing interest in studying the nonlinear PDEs on metric measure spaces. We propose to focus on first order Hamilton-Jacobi equations and investigate the well-posedness on metric spaces.
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| 研究実績の概要 |
The first project studies the discontinuous eikonal equation in metric measure spaces. Besides uniqueness and existence results for the associated Dirichlet boundary, we obtain the regularity of the unique solution under suitable assumptions.
The second project is concerned with a PDE approach to horizontally quasiconvex functions in the Heisenberg group based on a nonlinear second order elliptic operator. We discuss sufficient conditions and necessary conditions for upper semicontinuous, h-quasiconvex functions in terms of the viscosity subsolution to the associated elliptic equation.
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