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

Abstract:

      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 .