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Estimates of eigenfunctions of elliptic operators with constant coefficients

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Abstract

The Dirichlet problem for a symmetric elliptic operator with constant coefficients is studied. Estimates of the moduli of normalized eigenfunctions, uniform in a closed region, are obtained. These estimates generalize certain results of Kh. L. Smolitskii, O. A. Ladyzhenskaya, L. N. Slobodetskii, D. M. Éidus, V. A. Il'in, and I. A. Shishmarev.

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Authors
  1. Yu. V. Egorov
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  2. V. A. Kondrat'ev
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Additional information

Translated from Trudy Seminara im. I. G. Petrovskogo, No. 12, pp. 229–237, 1987.

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Egorov, Y.V., Kondrat'ev, V.A. Estimates of eigenfunctions of elliptic operators with constant coefficients. J Math Sci 47, 2660–2667 (1989). https://doi.org/10.1007/BF01105916

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  • DOI: https://doi.org/10.1007/BF01105916

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