【115/4/28】16:10-17:00 Prof. Mikko Salo (University of Jyvaskyla)
發佈日期 :
2026-04-24
| Analysis Seminar | |
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| Time | 2026-4-28 16:10-17:00 |
| Venue | 數學館3樓 31301 教室 |
| Speaker | Prof. Mikko Salo (University of Jyvaskyla) |
| Title | The Plane Wave Method |
| Abstract | The inverse problem of Calder´on, in its geometric formulation, asks if a Riemannian metric in a domain is determined up to isometry by boundary measurements of harmonic functions. Physically this corresponds to determining a matrix electrical conductivity function from voltage and current measurements on the boundary. This problem is open in general. In this talk we will discuss the hyperbolic analogue of the Calder´on problem, involving the (Lorentzian) wave equation in various settings. For time-independent coefficients this boils down to the classical Gel’fand or inverse boundary spectral problem, and there is a large literature since the 1980s based on the Boundary Control and geometrical optics methods. Recently, a new method has been introduced for hyperbolic inverse problems. The method is based on (distorted) plane waves, and it involves Carleman estimates in the spirit of the Bukhgeim-Klibanov method. This method applies to certain formally determined inverse problems also with time-dependent coefficients. In this talk I will attempt to explain the basic ideas behind the plane wave method and the results obtained in this way. This talk is based on joint work with L. Oksanen (Helsinki) and Rakesh (Delaware). |
