摘要
四阶变分不等式解的正则性多年来一直是人们关心的课题.对于具有位移障碍的四阶变分不等式,[1]、[2]、[3]得到了其解的H^3-正则性和C^2-正则性.那么,对它来说能否得到更好的正则性(如H^4-正则性)呢?它的极限正则性又是多少呢?数值分析学家们则希望能有较好的正则性结果(如有H^4-正则性),以便能使近似解(如有限元解)有满意的误差估计.本文将试图通过一个例子来考察这一问题,并指出了具有位移障碍且边界强制的四阶变分不等式解的极限正则性.这个例子将说明:即使所有的已知数据(如边界,系数等)
An example of a fourth order variational inequality is structed in this note. The example shows; u∈H3+a(Ω) with every ο<0.5(but μ H//3.5(Ω)) is limiting re-gularity of solution u of a fourth order variational inequality with displacement obstacle.
