Uniqueness, non-uniqueness and conditional stability ofsolutions to the Cauchy problem for degenerate ellipticdifferential equations with low-regular coefficients

最近，申请人获得了关于低正则系数的向后抛物和椭圆算子的唯一性和条件稳定性的最优结果。这些考虑的主要工具是使用准微分技术。该项目是针对退化椭圆微分算子的问题。主要目的是了解变阶特征对低正则系数算子的唯一性和条件稳定性的影响。此外，还应构造反例来回答结果的最优性问题。主要的工具是开发合适的para-differential微积分加上区域的方法。

Recently, the applicants obtained optimal results concerning uniqueness and conditional stability for backward parabolic and elliptic operators with low regular coefficients. The main tool of these considerations is the use of para-differential techniques. The project is addressed to the issue of degenerate elliptic differential operators. The main goal is to understand the influence of characteristics of variable order on uniqueness and conditional stability for such operators with low regular coefficients. Besides, counter-examples shall be constructed which may serve to answer the question for optimality of the results. The main tool is to develop suitable para-differential calculus coupled with the method of zones.