具有次临界增长的椭圆障碍问题解的正则性  

Regularity for solutions of elliptic obstacle problems with subcritical growth

作　　者：杜广伟[1] DU Guang-wei(Department of Mathematics, Northwestern Polytechnical University, Xi＇an 710129, Shaanxi, China)

机构地区：[1]西北工业大学数学系,陕西西安710129

出　　处：《山东大学学报（理学版）》2018年第6期57-63,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11771354);陕西省自然科学基础研究计划资助项目(2017JM5140)

摘　　要：利用一个改进的p-调和逼近引理,首先证明了具有次临界增长的p-Laplace型拟线性椭圆障碍问题解的梯度的Morrey正则性。进一步地,利用Hlder连续函数的积分刻划引理得到了解的Hlder连续性。利用该方法避免了证明梯度的反向不等式,从而简化了证明。Based on a modification of p-harmonic approximation argument,the gradients of solutions to the quasilinear elliptic p-Laplace type obstacle problems with subcritical growth enjoy the Morrey regularity are proved. Then the Hlder continuity of solutions is obtained by using the integral characterization of Hlder continuous functions. Making use of this method,one can simplify the proof avoiding the proof of a suitable reverse Hlder inequality for the gradient.

关 键 词：椭圆障碍问题 次临界增长 Morrey正则性 HOLDER连续性 

分 类 号：O175.2[理学—数学]