Estimates of derivative solutions of linear parabolic equations with special singularities on the boundary of the Hölder norm domain (Q1901874)

We obtain boundary estimates of the maximum modulus and Hölder norms of the gradient of bounded solutions of the homogeneous Dirichlet problem for a uniformly parabolic linear equation with a ``composite'' right-hand side and coefficients at lower derivatives: \[ Lu= f_1+ f_2\quad\text{in} \quad Q= \Omega\times ]0; T[,\quad u= 0\quad\text{on} \quad \partial\Omega\times ]0; T[. \] Here, \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with boundary \(\partial\Omega\in W^2_{q+ 2}\), \(q> n\).