Smoothness of solutions of the Cauchy problem for degenerate parabolic equations
The Cauchy problem is considered \[ \partial_ tu=Au\quad (t>0),\quad u|_{t=0}=f. \] Here A is a linear selfadjoint nonnegative second- order differential operator with analytic coefficients. Growth estimates for derivatives of solutions with respect to x variables are obtained. An example of an A operator is given, for which these estimates are precise.
scientific article; zbMATH DE number 4042420