关于ut= div(|▽u|p-2▽u)方程解的梯度H?lder连续性的一个注记(英文)

A Note on H?lder Continuity of the Gradient of the Solutions for ut= div(|▽u|p-2▽u)

英文关键词:H?lder continuity of the gradient  weak solution.

中文摘要:

      对文献［１－３］中的结果：u_t= div(|▽u|^p-2▽u)在ΩＴ＝Ω×（０，Ｔ）上弱解的空间梯度是Ｈ?ｌｄｅｒ连续的做一个补充．在这个注记里，讨论了条件ｐ＞ｍａｘ｛１，２Ｎ/Ｎ＋２｝是怎样由ｕ的性质所决定的．属于L^N_loc(Ω_T)空间解的梯度是Ｈ?ｌｄｅｒ连续的条件仅仅是ｐ＞１．

英文摘要:

      In , H?lder continuity for the spatial gradient of weak solutions ofu_t= div(|▽u|^p-2▽u) in Ω_T= Ω×(0,T) was established, where ▽= grad x, Ω(?)R^N. We discuss here how the conditionp> max {1, 2N/N+2 }is determined by the behaviour of u . Theorem implies that for solution in L^N_loc(Ω_T), the condition for the gradient of solution being H?lder continuous needs only p>1 .