Nodal sets for sums of eigenfunctions on Riemannian manifolds
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- by Harold Donnelly PDF
- Proc. Amer. Math. Soc. 121 (1994), 967-973 Request permission
Abstract:
Quantitative versions of unique continuation are proved for finite sums of eigenfunctions of the Laplacian on compact Riemannian manifolds. The results include a lower bound for the order of vanishing, a growth estimate for the supremum on compact balls, and a gradient bound. For real analytic metrics, an upper bound for the Hausdorff measure of the zero set is derived.References
- N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. (9) 36 (1957), 235–249. MR 92067
- H. O. Cordes, Über die eindeutige Bestimmtheit der Lösungen elliptischer Differentialgleichungen durch Anfangsvorgaben, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. IIa. 1956 (1956), 239–258 (German). MR 0086237
- Harold Donnelly and Charles Fefferman, Nodal sets of eigenfunctions on Riemannian manifolds, Invent. Math. 93 (1988), no. 1, 161–183. MR 943927, DOI 10.1007/BF01393691
- Lars Hörmander, Linear partial differential operators, Die Grundlehren der mathematischen Wissenschaften, Band 116, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0161012
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 967-973
- MSC: Primary 58G25
- DOI: https://doi.org/10.1090/S0002-9939-1994-1205487-X
- MathSciNet review: 1205487