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

低正则系数简并椭圆微分方程柯西问题解的唯一性、非唯一性和条件稳定性

• 批准号: 278164640
• 负责人: Professor Dr. Michael Reissig
• 金额: --
• 依托单位: Institut für Angewandte Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/278164640?language=en
• 关键词: Uniqueness; non; uniqueness; conditional; stability

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.

最近，申请人获得了关于具有低正则系数的后向抛物线和椭圆算子的唯一性和条件稳定性的最佳结果。这些考虑的主要工具是准微分技术的使用。该项目致力于解决退化椭圆微分算子的问题。主要目标是了解变量阶数特征对此类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，以回答结果最优性的问题。主要工具是开发合适的拟微分微积分与区域方法相结合。

项目成果

Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation, II

具有功率非线性和尺度不变的时间相关质量和耗散的半线性波模型，II

• DOI: 10.1002/mana.201700144
• 发表时间: 2018
• 期刊: Mathematische Nachrichten
• 影响因子: 1
• 作者: Palmieri;Alessandro;Reissig;Michael
• 通讯作者: Michael