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 Mat. Sb., 2000, Volume 191, Number 3, Pages 113–142 (Mi msb465)

Unique continuation of solutions of differential equations with weighted derivatives

N. A. Shananin

Peoples Friendship University of Russia

Abstract: The paper contains a generalization of Calderon's theorem on the local uniqueness of the solutions of the Cauchy problem for differential equations with weighted derivatives. Anisotropic estimates of Carleman type are obtained. A class of differential equations with weighted derivatives is distinguished in which germs of solutions have unique continuation with respect to part of the variables.

DOI: https://doi.org/10.4213/sm465

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English version:
Sbornik: Mathematics, 2000, 191:3, 431–458

Bibliographic databases:

UDC: 517.85
MSC: Primary 35A07, 35G10; Secondary 35SXX

Citation: N. A. Shananin, “Unique continuation of solutions of differential equations with weighted derivatives”, Mat. Sb., 191:3 (2000), 113–142; Sb. Math., 191:3 (2000), 431–458

Citation in format AMSBIB
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• https://doi.org/10.4213/sm465
• http://mi.mathnet.ru/eng/msb/v191/i3/p113

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. A. Shananin, “Partial quasianalyticity of distribution solutions of weakly nonlinear differential equations with weights assigned to derivatives”, Math. Notes, 68:4 (2000), 519–527
2. N. A. Shananin, “Propagation of the Invariance of Germs of Solutions of Quasilinear Differential Equations with Weighted Derivatives”, Math. Notes, 71:1 (2002), 123–130
3. Shananin, NA, “On propagation of germ invariance”, Acta Applicandae Mathematicae, 72:1–2 (2002), 101
4. N. A. Shananin, “On the Fiber Structure of Symmetry Invariance Sets of Solutions to Quasilinear Equations”, Math. Notes, 88:6 (2010), 879–887
5. N. A. Shananin, “On the Unique Continuation along Curves of Germs of Solutions to Linear Differential Equations with Constant Coefficients”, Math. Notes, 102:1 (2017), 128–132
6. N. A. Shananin, “On the Unique Continuation of the Germs of Solutions of First-Order Differential Equations along Curves”, Math. Notes, 102:6 (2017), 855–866
7. Levin A., “Difference Dimension Quasi-Polynomials”, Adv. Appl. Math., 89 (2017), 1–17
8. Levin A., “Bivariate Dimension Quasi-Polynomials of Difference-Differential Field Extensions With Weighted Basic Operators”, Math. Comput. Sci., 13:1-2, SI (2019), 157–168
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