Unimprovability of estimates of hÖlder constants for solutions of linear elliptic equations with measurable coefficients

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Abstract

The author considers the validity of an estimate in the norm of the Holder spaces Cs for the solutions of linear elliptic equations estimate does not depend on the smoothness of the coefficients It is known (MR 83c:35059) that such an estimate holds for sufficiently small exponents (0, 1) depending on ç and v. In this paper it is proved that this dependence is essential: For every 6 (0, 1) one can exhibit a constant (0, 1) and construct a sequence in £3 of elliptic equations, of the indicated form with smooth coefficients, whose solutions converge uniformly in the unit ball to a function that does not belong.

Original languageEnglish (US)
Pages (from-to)269-281
Number of pages13
JournalMathematics of the USSR - Sbornik
Volume60
Issue number1
DOIs
StatePublished - Feb 28 1988

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