摘要
本文研究了下述障碍问题这里,(?)_φ^+={v∈C(G)∩W^(1,p)(G),v—φ∈W^(1,p)(G),且v≥φ},G是R^n中有界区域。在p∈(1,2)的情形,我们证实了Lindqvist的一个猜想,即如果障碍函数φ的梯度局部H(?)lder连续,则障碍问题的解梯度也是局部H(?)lder连续。
In this paper, we study following obstacle problem: ∫_σ|▽v|'dx=min (?)v∈F_φ^+ where F_φ^+={v∈C(G)∩W^(1,p)(G), v-φ∈W_0^(1,p)(G), and v≥φ). G is a boundary domain in R^(?). In the case of p∈(1,2), Lindqvist's hYpothesis is proved, that is: if the obstacle function φ∈C_(loc)^(1,α), then the solution of the above problem is C_(loc)^(1,α) too, where α_1 depends on α and some other constants.
关键词
障碍问题
正则性
HOELDER连续
regularity of solution, obstacle problem, Holder continuous, variational ineguality
