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On the Interior Smoothness of Solutions to Second-Order Elliptic Equations

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Abstract

We study the interior smoothness properties of solutions to a linear second-order uniformly elliptic equation in selfadjoint form without lower-order terms and with measurable bounded coefficients. In terms of membership in a special function space we combine and supplement some properties of solutions such as membership in the Sobolev space W 12, loc and Holder continuity. We show that the membership of solutions in the introduced space which we establish in this article gives some new properties that do not follow from Holder continuity and the membership in W 12,loc .

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Authors and Affiliations

  1. Steklov Mathematical Institute, Moscow, Russia

    A. K. Gushchin

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  1. A. K. Gushchin
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Additional information

Original Russian Text Copyright © 2005 Gushchin A. K.

The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00377) and the State Maintenance Programs for the Junior Scientists and Leading Scientific Schools of the Russian Federation (Grant NSh-1542.2003.1).

In memory of Tadei Ivanovich Zelenyak.

__________

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 1036–1052, September– October, 2005.

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Gushchin, A.K. On the Interior Smoothness of Solutions to Second-Order Elliptic Equations. Sib Math J 46, 826–840 (2005). https://doi.org/10.1007/s11202-005-0081-3

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  • DOI: https://doi.org/10.1007/s11202-005-0081-3

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