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Solution of boundary-value problems for elliptic equations in the space of distributions

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Abstract

We extend the well-known approach to solution of generalized boundary-value problems for second-order elliptic and parabolic equations and for second-order strongly elliptic systems of variational type to the case of a general normal boundary-value problem for an elliptic equation of order2m. The representation of a distribution from (C ∞ (S))’ is established and is usedfor the proof of convergence of an approximate method of solution of a normal elliptic boundary-value problem in unnormed spaces of distributions.

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Authors and Affiliations

  1. Lvov University, Lvov

    G. P. Lopushanskaya

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  1. G. P. Lopushanskaya
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.51, No. 2, pp. 190–203, February, 1999.

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Lopushanskaya, G.P. Solution of boundary-value problems for elliptic equations in the space of distributions. Ukr Math J 51, 208–223 (1999). https://doi.org/10.1007/BF02513474

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  • DOI: https://doi.org/10.1007/BF02513474

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