TY - JOUR

T1 - Unimprovability of estimates of hÖlder constants for solutions of linear elliptic equations with measurable coefficients

AU - Safonov, M. V.

PY - 1988/2/28

Y1 - 1988/2/28

N2 - 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.

AB - 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.

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U2 - 10.1070/SM1988v060n01ABEH003167

DO - 10.1070/SM1988v060n01ABEH003167

M3 - Article

AN - SCOPUS:0009315148

SN - 0025-5734

VL - 60

SP - 269

EP - 281

JO - Mathematics of the USSR - Sbornik

JF - Mathematics of the USSR - Sbornik

IS - 1

ER -