An upper estimate of solution for a general class of parabolic equations (Q2704332)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An upper estimate of solution for a general class of parabolic equations |
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21 October 2001
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estimate on the \(L^\infty\) norm
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integro-differential inequalities
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An upper estimate of solution for a general class of parabolic equations (English)
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The authors prove an estimate on the \(L^\infty\) norm of solutions of parabolic differential equations in divergence form. Such estimates are well known [see, for example, \textit{D. G. Aronson} and \textit{J. Serrin}, Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 21, 291-305 (1967; Zbl 0148.34803)] for power nonlinearities. The new ingredient here is the consideration of nonpower laws such as in the reviewer's paper [Commun. Partial Differ. Equations 16, 311-361 (1991; Zbl 0742.35028)].
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