Unique continuation problems and complex phase methods in the theory of partial differential equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540185
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: TAKASHI OKAJI 京都大学, 理学(系)研究科(研究院), 准教授 (20160426)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 解の一意接続性 / ディラック作用素 / 放物型方程式 / スペクトル問題

Outline of Final Research Achievements

We investigated spectral properties of Dirac operators for the relativistic particles like electrons and obtained important results on its essential self-adjointness and the absence of eigenvalues at the thresholds. Moreover, we established the strong unique continuation property for parabolic operators of second order with singular potentials. In addition, we revealed a global structure of the singularities of solutions to the Cauchy problem for a partial differential equation in the whole complex domain.

Free Research Field

偏微分方程式論