具间断系数拟线性退化椭圆方程在可控增长下的正则性  

REGULARITY OF A CLASS OF DEGENERATE ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS UNDER CONTROLLABLE GROWTH

作　　者：郑神州[1] 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《系统科学与数学》2012年第5期549-561,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11071012)资助课题

摘　　要：对于具有VMO间断系数的散度型拟线性退化椭圆型方程,考虑了低阶项微分项在可控制增长条件下的弱解梯度的Morrey空间L^(p,λ)局部正则性,从而在已知数据正则性提高的条件下得到弱解具有优化Hlder指数的Hlder连续性结果。In this paper, we are concerned with the regularity in Morrey space for the derivative of weak solutions of a class of degenerate elliptic equations when the coefficient matrice A（x, u） satisfies certain VMO conditions in x uniformly with respect to u, and the lower order term satisfies controllable growth. Also, an interior HSlder continuity of its solutions is derived with the improvement of given g（x）.

关 键 词：可控增长 VMO间断系数 退化椭圆 逆向Hlder不等式 

分 类 号：O175.25[理学—数学]