Mathematical Sciences: "Unique Continuation, Quantitative Properties of Solutions and Symmetry for PDE's

本项目将研究次椭圆的唯一延拓问题 算子、Wiener准则和Harnack不等式， 边值问题的对称性 唯一的延续， 亚椭圆算子将通过混合研究 几何和变分技术，允许更多的情况下， 通常的Carleman方法。 在对称性的研究中， 他将继续尝试解决希弗的 Pompeiu's Problem的问题 这个项目要考虑的问题是有动机的 几何和数学物理中的基本问题。 他们的 答案将有助于更坚定地理解基本的 科学问题。

This project will study unique continuation for subelliptic operators, Wiener's criterion and Harnack inequalities, and symmetry of boundary value problems. Unique continuation for subelliptic operators will be studied through a blend of geometric and variational techniques that allow more cases than the usual Carleman method. In the studies of symmetries the PI will continue his attempts in the solution to Schiffer's conjecture and Pompeiu's problem. The questions to be considered in this project are motivated by basic problems in geometry and mathematical physics. Their answers will contribute to a firmer understanding of fundamental scientific issues.