Uniqueness, non-uniqueness and conditional stability of solutions to the Cauchy problem for degenerate elliptic differential equations with low-regular coefficients

• Applicant: Professor Dr. Michael Reissig
• Subject Area: Mathematics
• Term: from 2015 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 278164640

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.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Dr. Karen Yagdjian