中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Mikko Salo (University of Jyvaskyla, Finland)
题 目："Inverse problems for elliptic PDE"(1)
时 间：2023.11.20（星期一）15:00-15:50
地 点：晨兴楼510
Zoom ID: 840 6884 1907 Code: AMSS2023
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题 目: "Inverse problems for elliptic PDE" (2)
时 间：2023.11.20（星期一）16:00-16:50
地 点：晨兴楼510
Zoom ID: 840 6884 1907 Code: AMSS2023
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题 目: "Inverse problems for elliptic PDE" (3)
时 间：2023.11.21（星期二）15:00-15:50
地 点：晨兴楼510
Zoom ID: 840 6884 1907 Code: AMSS2023
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题 目: "Inverse problems for elliptic PDE" (4)
时 间：2023.11.21（星期二）16:00-16:50
地 点：晨兴楼510
Zoom ID: 840 6884 1907 Code: AMSS2023
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题 目："Inverse problems for elliptic PDE" (5)
时 间：2023.11.23（星期四）15:00-15:50
地 点：晨兴楼510
Zoom ID: 840 6884 1907 Code: AMSS2023
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题 目: "Inverse problems for elliptic PDE" (6)
时 间：2023.11.23（星期四）16:00-16:50
地 点：晨兴楼510
Zoom ID: 840 6884 1907 Code: AMSS2023
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题 目："Inverse problems for elliptic PDE" (7)
时 间：2023.11.24（星期五）15:00-15:50
地 点：晨兴楼510
Zoom ID: 840 6884 1907 Code: AMSS2023
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题 目: "Inverse problems for elliptic PDE" (8)
时 间：2023.11.24（星期五）16:00-16:50
地 点：晨兴楼510
Zoom ID: 840 6884 1907 Code: AMSS2023
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摘 要：This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and medical imaging and forms the mathematical model for Electrical Impedance Tomography. In this problem, the objective is to determine an unknown coefficient (electrical conductivity) in an elliptic PDE from boundary measurements of its solutions (voltage and current measurements).
The lectures will begin with an introduction to the Calderon problem and classical uniqueness results. We will then study the geometric, or anisotropic, Calderón problem which will involve a little bit of Riemannian geometry. In the last part of the lectures we will consider recent results in inverse problems for nonlinear elliptic PDE. The methods discussed in the lectures will include weak solutions, Carleman estimates, geometrical optics, higher order linearisation for semilinear equations, and p-Laplace type equations. We will also mention several open problems.
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