收稿日期: 2012-01-09
修回日期: 2012-05-07
网络出版日期: 2012-05-07
基金资助
Supported by National Natural Science Foundation of China(11001221), Mathematical Tianyuan Foundation of China (11126027) and Northwestern Polytechnical University Jichu Yanjiu Jijin Tansuo Xiangmu(JC201124)
Higher integrability result for solutions to nondivergence elliptic equations with low-order terms
Received date: 2012-01-09
Revised date: 2012-05-07
Online published: 2012-05-07
白晋彦 , 崔学伟 . 带有低阶项的非散度椭圆方程解的二阶导数的高阶可积性[J]. 中国科学院大学学报, 2013 , 30(3) : 293 -297 . DOI: 10.7523/j.issn.1002-1175.2013.03.002
We establish a higher integrability for second derivatives of solutions to the nondivergence elliptic equations of the following type
,
where the coefficients aij(x) are bounded and have small BMO-norm, and bi(x) and c(x) belong to Ln(Ω) where Ω is a bounded smooth domain in Rn(n≥3).
[1] Campanato S. Un risultato relativeo ad equazioni ellittiche del secondo ordine di tipo non variazionale[J]. Ann Scuola Norm Sup Pisa, 1967, 21(4): 701-707.
[2] Meyers N G. An Lp estimate for the gradient of solutions of second order elliptic divergence equations[J]. Ann Sc Norm Sup Pisa, 1963, 17(3):189-206.
[3] Franciosi M, Moscariello G. Higher integrability results[J]. Manus Math, 1985, 52(1-3):151-170.
[4] Pagano A. Higher integrability for minimizers of variational integrals with nonstandard growth[J]. Mathematics and Statistics, 1993,39(1): 1-17.
[5] Dibenedetto E, Manfredi J. On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems[J]. Amer J Math, 1993, 115(5): 1107-1134.
[6] Esposito L, Leonetti F, Mingione G. Higher integrability for minimizers of integral functionals with (P, Q) growth[J]. J Diff Eqs, 1999, 57(2): 414-438.
[7] Radice T. A higher integrability result for nondivergence elliptic equations[J]. Annali di Matematica, 2008, 187(1): 93-103.
[8] Fusco N, Sbordone C. Higher integrability of the gradient of minimizers of functionals with nonstandard growth conditions[J]. Comm Pure Appl Math, 1990,43(5): 673-683.
[9] Coifman R, Lions P L, Meyer Y, et al. Compensated compactness and Hardy spaces[J]. J Math Pures Appl, 1993, 72(9): 247-286.
[10] Wu Z Q, Yi J X, Wang C P. An introduction to Elliptic and Parabolic equations[M]. Beijing: Science Press, 2003:12-16.
[11] Bramanti M, Brandolini L. Lp estimate for uniformly hypoelliptic operators with discontinuous coefficients on homogeneous groups[J]. Rend Sem Mat Univ Pol Torino, 2000, 58(4):389-433.
[12] Cohn W S, Lu G Z, Wang P Y. Sub-elliptic global high order Poincaré inequalities in stratified Lie groups and applications[J]. J Funct Anal, 2007, 249(2): 393-424.
[13] Lu G Z. Polynomials, higher order Sobolev extension theorems and interpolation inequalities on weighted Folland-Stein spaces on stratified groups[J]. Acta Math Sinica (Engl Ser), 2000, 16(3): 405-444.
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