Abstract
We study C 2,1 nonnegative solutions u(x,t) of the nonlinear parabolic inequalities
in a punctured neighborhood of the origin in \({\bf R}^n \times [0,\infty)\), when \(n\ge 1\) and \(\lambda > 0\). We show that a necessary and sufficient condition on λ for such solutions u to satisfy an a priori bound near the origin is \(\lambda\le \frac{n+2}n\), and in this case, the a priori bound on u is
This a priori bound for u can be improved by imposing an upper bound on the initial condition of u.
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Taliaferro, S.D. Isolated singularities of nonlinear parabolic inequalities. Math. Ann. 338, 555–586 (2007). https://doi.org/10.1007/s00208-007-0088-0
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DOI: https://doi.org/10.1007/s00208-007-0088-0