Isolated singularities of nonlinear parabolic inequalities
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We study C 2,1 nonnegative solutions u(x,t) of the nonlinear parabolic inequalities in a punctured neighborhood of the origin in, when >. We show that a necessary and sufficient condition on for such solutions u to satisfy an a priori bound near the origin is, and in this case, the a priori bound on u is u(x,t) = O > 0. This a priori bound for u can be improved by imposing an upper bound on the initial condition of u. Springer-Verlag 2007.
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