# Unique continuation of solutions of differential equations with weighted derivatives

## 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.

- Authors:

- Peoples Friendship University of Russia, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21202929

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 191; Journal Issue: 3; Other Information: DOI: 10.1070/SM2000v191n03ABEH000465; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; CAUCHY PROBLEM; DIFFERENTIAL EQUATIONS; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Shananin, N A.
```*Unique continuation of solutions of differential equations with weighted derivatives*. United States: N. p., 2000.
Web. doi:10.1070/SM2000V191N03ABEH000465; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Shananin, N A.
```*Unique continuation of solutions of differential equations with weighted derivatives*. United States. doi:10.1070/SM2000V191N03ABEH000465; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Shananin, N A. Sun .
"Unique continuation of solutions of differential equations with weighted derivatives". United States. doi:10.1070/SM2000V191N03ABEH000465; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21202929,
```

title = {Unique continuation of solutions of differential equations with weighted derivatives},

author = {Shananin, N A},

abstractNote = {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 = {10.1070/SM2000V191N03ABEH000465; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 3,

volume = 191,

place = {United States},

year = {2000},

month = {4}

}

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