Regularity of solutions of boundary value problems for parabolic equations of arbitrary order in weighted Hölder spaces
М. Ф. Черепова · Differential Equations · 2014
We consider initial-boundary value problems for a uniformly parabolic equation of arbitrary order 2 m in a noncylindrical domain whose lateral boundary is nonsmooth with respect to t . We assume that the lower-order coefficients and the right-hand side of the equation, generally speaking, grow to infinity no more rapidly than some power function when approaching the parabolic boundary of the domain, all coefficients of the equation are locally Hölder, and their Hölder constants can grow near that boundary. We construct a smoothness scale of solutions of such problems in weighted Hölder classes of functions whose higher derivatives may grow when approaching the parabolic boundary of the domain.