摘要
Consider the Cauchy problem for the evolution p Laplacian equation[HL(2:0,2Z;1,Z]ut=div(|u| p-2 u),(x,t)∈Q T=R n×(0,T), u(x,0)=u 0(x)∈L ∞(R N),x∈R N.In terms of the uniform estimates to the regulized solutions of the problem above, we prove that u x j ∈c β,β/(1+β) loc (Q T), where the Hlder exponent with respect to t is great than β2.
Consider the Cauchy problem for the evolution p Laplacian equation[HL(2:0,2Z;1,Z]ut=div(|u| p-2 u),(x,t)∈Q T=R n×(0,T), u(x,0)=u 0(x)∈L ∞(R N),x∈R N.In terms of the uniform estimates to the regulized solutions of the problem above, we prove that u x j ∈c β,β/(1+β) loc (Q T), where the Hlder exponent with respect to t is great than β2.
