On the solvability of the characteristic Dirichlet problem for linear degenerate parabolic equations
N. D. Kutev, Alessandro Oliaro, Petar Popivanov · Proceedings of the American Mathematical Society · 2010
We investigate the classical solvability for some classes of linear, degenerate equations in divergence form with prescribed Dirichlet data. Since the boundary value problem is characteristic according to Fichera on a part of the boundary, some typical nonlinear phenomena at these points are observed as boundary gradient blowups of the classical solutions in space directions. The regularity results explain the lack of hypoellipticity for special right-hand sides or boundary data for linear degenerate parabolic equations.