Abstract: | One considers singular parabolic equations of the form ![part](/content/x774v674t7q6h057/xxlarge8706.gif) (u)/ t– u 0,where sign u is a multivalued function, equal to -I for u<0, to 1 for u>0, and to the segment -I,I] for u=0. Such a class of equations contains, in particular, the model for the two-phase Stefan problem, the porous medium equation, and the plasma equation. For the bounded generalized solutions u(x,t) of the indicated equations (without the assumption u/![part](/content/x774v674t7q6h057/xxlarge8706.gif) L2one has established a qualified local estimate of the modulus of continuity.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Ins'tituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 49–71, 1985. |