Abstract
In this article we study some limiting cases of strong unique continuation for inequalities of the type
or
where Ω is a neighbourhood of the origin in R n, and A, B, C are positive constants.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Alinhac and M.S. Baouendi, Uniqueness for the characteristic Cauchy problem and strong unique continuation for higher order partial differential inequalities, Amer. J. Math. 102 (1980), 179–217.
S. Alinhac and M.S.Baouendi, A counterexample to strong uniqueness for partial differential equations of Schrödinger’s type Comm. Partial Differential Equations 19 (1994), 1727–1733.
B. Barcelo, C.E. Kenig, A. Ruiz, and C.D. Sogge, Weighted Sobolev inequalities for the Laplacian plus lower order terms Illinois J. Math. 32 (1988), 230–245.
F. Colombini and C. Grammatico, Some remarks on strong unique continuation for the Laplace operator and its powers Comm. Partial Differential Equations 24 (1999), 1079–1094.
F. Colombini and C. Grammatico, A counterexample to strong uniqueness for all powers of the Laplace operator Comm. Partial Differential Equations 25 (2000), 585–600.
C. Grammatico, A result on strong unique continuation for the Laplace operator Comm. Partial Differential Equations 22 (1997), 1475–1491.
L. Hörmander, Uniqueness theorems for second order elliptic differential equations Comm. Partial Differential Equations 8 (1983), 21–64.
D. Jerison and C.E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operator Ann. of Math. 121 (1985), 463–494.
P. Le Borgne, Unicité forte pour le produit de deux opérateurs elliptiques d’ordre 2, Indiana Univ. Math. J. 50 (2001); (http://inca.math.indiana.edu/iumj/Papers/renderToc.php3)
R. Regbaoui, Strong continuation for second order elliptic differential operators J. Differential Equations 141 (1997), 201–217.
T. Wolff, A counterexample in a unique continuation problem Comm. Anal. Ceom. 2 (1994), 79–102.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Colombini, F., Grammatico, C. (2001). Strong Uniqueness for Laplace and Bi-Laplace Operators in the Limit Case. In: Colombini, F., Zuily, C. (eds) Carleman Estimates and Applications to Uniqueness and Control Theory. Progress in Nonlinear Differential Equations and Their Applications, vol 46. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0203-5_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0203-5_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6660-0
Online ISBN: 978-1-4612-0203-5
eBook Packages: Springer Book Archive