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Статья
2015

Inner uniqueness theorem for second order linear elliptic equation with constant coefficients


I. A. BikchantaevI. A. Bikchantaev
Русская математика
https://doi.org/10.3103/S1066369X15050023
Abstract / Full Text

We consider solution f to a linear elliptic differential equation of second order, and prove that it vanishes if zeros of f condense to two points along non-collinear rays. The requirement of non-collinearity of the rays is essential if the roots of the characteristic equation are distinct. In the case of equal roots of the characteristic equation this property is valid if and only if the rays do not belong to common straight line.

Author information
  • Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, RussiaI. A. Bikchantaev
References
  1. Hörmander, L. “Uniqueness Theorems for Second Order Elliptic Differential Equations,” Comm. Partial Differ. Equat. 8, No. 1, 21–64 (1983).
  2. Meshkov, V. Z. “A Uniqueness Theorem for Second-Order Elliptic Equations,” Mat. Sb. 129, No. 3, 386–396 (1986)
  3. Bikchantaev, I. A. “On Uniqueness Sets for an Elliptic Equation with Constant Coefficients,” Differ. Equ. 47, No. 2, 278–282 (2011).
  4. Bitsadze, A. V. Boundary-Value Problems for Second Order Elliptic Equations (Nauka, Moscow, 1966) [in Russian].