Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 137)
Unique Continuation Problems for Partial Differential Equations
The aim of this article is to give an overview of the main problems and results in unique continuation. Broadly speaking, an unique continuation result is any statement of the following type:
Given a linear partial differential operator P and two regions A C B, a solution u to Pu = 0 is uniquely determined in the larger set B by its values (behavior) in the smaller set A.
KeywordsPoisson Bracket Oriented Surface Principal Symbol Infinite Order Unique Continuation
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- N. Aronszajn. A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. (9), 36: 235–249, 1957.Google Scholar
- Lars Hörmander. On the uniqueness of the Cauchy problem under partial analyticity assumptions, unpublished.Google Scholar
- Lars Hörmander. The analysis of linear partial differential operators. IV.Springer-Ver lag, Berlin, 1985. Fourier integral operators. Google Scholar
© Springer-Verlag New York, Inc. 2004