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On the Unique Continuation Properties for Elliptic Operators with Singular Potentials.
- Source :
- Acta Mathematica Sinica; Feb2007, Vol. 23 Issue 2, p297-308, 12p
- Publication Year :
- 2007
-
Abstract
- Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato–Fefferman–Phong’s class in Lipschitz domains. An elementary proof of the doubling property for u <superscript>2</superscript> over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the ℬ<subscript> p </subscript> weight properties for the solution u near the boundary. [ABSTRACT FROM AUTHOR]
- Subjects :
- EQUATIONS
ALGEBRA
MATHEMATICS
MATHEMATICAL functions
DIFFERENTIAL equations
Subjects
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 23
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 24487050
- Full Text :
- https://doi.org/10.1007/s10114-005-0869-x