I am looking at the IBVP: $$ u_t+x^2u_{xx}+u_y+f(x,y)=0, x,y \in D\in [0,\infty)\times[0,\infty),t\in(0,T]\\ $$$$ u(x,y,0)=F(x,y)\in C^{1,1}\\ $$$$ u(x,y,t)=0, x,y\in \partial D $$ and I would like to know the regularity of the solution of this PDE. According to Friedman's book the best I can hope is $C^{1,1,1}$. Any suggestions or references of higher derivatives result? Thanks!
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