|
Strong unique continuation for products of elliptic operators of second order
Author(s):
Ferruccio
Colombini;
Herbert
Koch
Journal:
Trans. Amer. Math. Soc.
362
(2010),
345-355.
MSC (2000):
Primary 35B60
Posted:
August 17, 2009
MathSciNet review:
2550154
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study strong unique continuation for products of elliptic operators. The main tools are Carleman inequalities for second order elliptic operators. We obtain strong unique continuation assuming either Gevrey regularity of the coefficients or some pointwise conditions on the coefficients.
References:
-
- 1.
- S. Alinhac.
Non-unicité pour des opérateurs différentiels à caractéristiques complexes simples.
Ann. Sci. École Norm. Sup. (4), 13(3):385-393, 1980. MR 597745 (83b:35004b) - 2.
- 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(1):179-217, 1980. MR 556891 (81e:35003) - 3.
- N. Aronszajn, A. Krzywicki, and J. Szarski.
A unique continuation theorem for exterior differential forms on Riemannian manifolds.
Ark. Mat., 4:417-453, 1962. MR 0140031 (25:3455) - 4.
- L. Boutet de Monvel and P. Krée. Pseudo-differential operators and Gevrey classes. Ann. Inst. Fourier (Grenoble), 17(fasc. 1):295-323, 1967. MR 0226170
- 5.
- T. Carleman.
Sur un problème d'unicité pur les systèmes d'équations aux dérivées partielles à deux variables indépendantes.
Ark. Mat. Astr. Fys., 26(17):9, 1939. MR 0000334 (1:55f) - 6.
- F. Colombini and C. Grammatico.
Some remarks on strong unique continuation for the Laplace operator and its powers.
Comm. Partial Differential Equations, 24(5-6):1079-1094, 1999. MR 1680873 (2000c:35263) - 7.
- F. Colombini and C. Grammatico.
A result on strong uniqueness in Gevrey spaces for some elliptic operators.
Comm. Partial Differential Equations, 30(1-3):39-57, 2005. MR 2131044 (2006c:35025) - 8.
- Ferruccio Colombini, Cataldo Grammatico, and Daniel Tataru.
Strong uniqueness for second order elliptic operators with Gevrey coefficients.
Math. Res. Lett., 13(1):15-27, 2006. MR 2199563 (2006j:35040) - 9.
- L. Hörmander. The analysis of linear partial differential operators. III, Springer-Verlag, 1985. MR 781536
- 10.
- Herbert Koch and Daniel Tataru.
Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients.
Comm. Pure Appl. Math., 54(3):339-360, 2001. MR 1809741 (2001m:35075) - 11.
- Philippe Le Borgne.
Unicité forte pour le produit de deux opérateurs elliptiques d'ordre 2.
Indiana Univ. Math. J., 50(1):353-381, 2001. MR 1857040 (2003i:35064) - 12.
- Nicolas Lerner.
Résultats d'unicité forte pour des opérateurs elliptiques à coefficients Gevrey.
Comm. Partial Differential Equations, 6, no. 10, 1163-1177, 1981. MR 632767 (83m:35063) - 13.
- Kinji Watanabe.
Sur l'unicité dans le problème de Cauchy pour les opérateurs différentiels à caractéristiques de multiplicité constante.
Tôhoku Math. J. (2), 31(2):151-164, 1979. MR 538916 (80g:35005) - 14.
- Claude Zuily.
Uniqueness and nonuniqueness in the Cauchy problem, volume 33 of Progress in Mathematics.
Birkhäuser Boston Inc., Boston, MA, 1983. MR 701544 (85d:35009)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
35B60
Retrieve articles in all Journals with
MSC (2000):
35B60
Additional Information:
Ferruccio
Colombini
Affiliation:
Department of Mathematics, University of Pisa, Via F Buonarroti 2, 56127 Pisa, Italy
Herbert
Koch
Affiliation:
Mathematisches Institut, University of Bonn, Beringstrasse 1, 53115 Bonn, Germany
DOI:
10.1090/S0002-9947-09-04799-0
PII:
S 0002-9947(09)04799-0
Received by editor(s):
September 21, 2007
Received by editor(s) in revised form:
January 15, 2008
Posted:
August 17, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
