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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 1989 Volume 180, Number 1, Pages 78–100 (Mi sm1598)

This article is cited in 13 papers

On boundedness of generalized solutions of elliptic differential equations with nonpower nonlinearities

A. G. Korolev


Abstract: Boundedness of generalized solutions of elliptic differential equations of divergence form with anisotropic nonpower nonlinearities is established. The proof of theorems on the boundedness of solutions is carried out by means of a further development of Moser's iteration technique; a preparatory feature is the derivation of an integral inequality of imbedding-theorem type for functions in anisotropic Sobolev–Orlicz spaces.
Bibliography: 28 titles.

UDC: 517.956

MSC: Primary 35J60, 35B35; Secondary 35J65

Received: 02.12.1986


 English version:
Mathematics of the USSR-Sbornik, 1990, 66:1, 83–106

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