A note on Krylov-Tso’s parabolic inequality
Luis Escauriaza · Proceedings of the American Mathematical Society · 1992
We show that if u u is a solution to ∑ i , j = 1 n a i j ( x , t ) D i j u ( x , t ) − D t u ( x , t ) = ϕ ( x ) \sum olimits _{i,j = 1}^n {{a_{ij}}(x,t){D_{ij}}u(x,t) - {D_t}u(x,t) = \phi (x)} on a cylinder Ω T = Ω × ( 0 , T ) {\Omega _T} = \Omega \times (0,T) , where Ω \Omega is a bounded open set in R n , T > 0 {{\mathbf {R}}^n},T > 0 , and u u vanishes continuously on the parabolic boundary of Ω T {\Omega _T} . Then the maximum of