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.
UR - http://www.scopus.com/inward/record.url?scp=0009315148&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0009315148&partnerID=8YFLogxK
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 -