2009 Fiscal Year Final Research Report

Strong unique continuation property and limiting absorption principle for partial differential systems with their applications

Research Project

Project/Area Number	18540173
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 Kyoto University, 大学院・理学研究科, 准教授 (20160426)
Co-Investigator(Renkei-kenkyūsha)	YAMADA Osanobu 立命館大学, 理工学部, 教授 (70066744)
Project Period (FY)	2006 – 2009
Keywords	偏微分方程式系 / 解の一意接続性 / 極限吸収原理 / ディラック作用素
Research Abstract	We investigate properties of solutions to system of equations including the Dirac equation which described the relativistic particles like electrons. In particular we establish that the Dirac equation with potential homogeneous of degree zero has only absolutely continuous spectra and it has no bound states if the velocity of light is large enough. Moreover we prove that the Stokes equation in fluid mechanics has strong unique continuation property even if its coefficients have strong singularities with critical order.

(5 results)