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Carleman inequalities and unique continuation for higher order elliptic differential operators

Citation

Wang, Wensheng (1993) Carleman inequalities and unique continuation for higher order elliptic differential operators. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:07192011-111928416

Abstract

In this thesis, we study the weak unique continuation property for higher order elliptic differential operators with real coefficients via Carleman inequalities. We get several Carleman inequalities with sharp gaps for operators in a reasonable class, which lead eventually to the weak unique continuation property for differential inequalities with optimal conditions on potentials. We also get some Carleman inequalities for general operators with simple or double characteristics. The gaps here are not as good as in the first case. But we may prove the gaps in these inequalities are sharp in general. Actually we will provide counterexamples to prove such gaps are sharp in Carleman inequalities for operators in some subclasses of simple or double characteristics class. In particular, we prove that there is no Carleman inequality with positive gap for the highest order term for any operator whose symbol has double characteristics.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Wolff, Thomas H.
Thesis Committee:
  • Unknown, Unknown
Defense Date:25 May 1993
Funders:
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Record Number:CaltechTHESIS:07192011-111928416
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:07192011-111928416
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6543
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:19 Jul 2011 21:12
Last Modified:26 Dec 2012 04:37

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