2023 Fiscal Year Annual Research Report
Hamilton-Jacobi equations on metric measure spaces
| Project/Area Number |
20K22315
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| Research Institution | Okinawa Institute of Science and Technology Graduate University |
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Principal Investigator |
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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| Project Period (FY) |
2020-09-11 – 2024-03-31
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| Keywords | eikonal equation / metric measure spaces / viscosity solution / discontinuous data / Heisenberg group / h-quasiconvex functions |
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| Outline of Annual Research Achievements |
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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Research Products
(8 results)
