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Elliptic boundary-value problems in nonsmooth domains

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Abstract

In a bounded domain, we study elliptic boundary-value problems for equations and systems of the Douglis-Nirenberg structure in complete scales of Banach spaces. The boundary of the domain contains conic points, edges, etc. A theorem on local increase in the smoothness of generalized solutions and a theorem on complete collection of isomorphisms are proved. Applications are considered. It is shown that the results obtained are also valid for transmission problems, nonlocal elliptic problems, elliptic problems with a parameter, and parabolic problems.

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Authors and Affiliations

  1. Chernigov Pedagogical Institute, Chernigov

    B. Ya. Roitberg & Ya. A. Roitberg

Authors
  1. B. Ya. Roitberg
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  2. Ya. A. Roitberg
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 701–709, May, 1995.

This research was partially supported by a grant of the American Mathematical Society and by the Ukrainian State Committee on Science and Technology.

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Roitberg, B.Y., Roitberg, Y.A. Elliptic boundary-value problems in nonsmooth domains. Ukr Math J 47, 808–817 (1995). https://doi.org/10.1007/BF01059054

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