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Splitting of the spectrum of the laplace operator on an ellipse with cuts


The exponential asymptotics with a factor of the semiclassical form multiplying the exponent is proved for the splitting of the eigenvalues of the the Laplace operator with the Dirichlet boundary condition in the case of an ellipse with cuts. The proof is based on the method of separation of variables.

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 173–178, 1989.

The author wishes to express his gratitude to V. F. Lazutkin for stimulating influence, interest in this work, and valuable comments.

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Terman, D.Y. Splitting of the spectrum of the laplace operator on an ellipse with cuts. J Math Sci 57, 3176–3180 (1991).

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  • Boundary Condition
  • Dirichlet Boundary
  • Laplace Operator
  • Dirichlet Boundary Condition
  • Exponential Asymptotics