A note to the regularity of solutions for the evolution \(p\)-Laplacian equations (Q1852692)
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scientific article; zbMATH DE number 1850442
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note to the regularity of solutions for the evolution \(p\)-Laplacian equations |
scientific article; zbMATH DE number 1850442 |
Statements
A note to the regularity of solutions for the evolution \(p\)-Laplacian equations (English)
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14 December 2003
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Initial (and initial-boundary) problem for the equation \[ u_t = \text{div} (|D u|^{p-2} D u) \] with \(p>2\) is considered. The Hölder continuity of \(D u\) and local boundedness of \(u_t\) are proved. Such results were known [\textit{E. Di Benedetto} and \textit{A. Friedman}, J. Reine Angew. Math. 357, 1-22 (1985; Zbl 0549.35061)], but the author propose another, simple proof.
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regularity of solutions
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nonlinear parabolic equations
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evolution p-Laplacian
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Hölder continuity of \(Du\)
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local boundedness of \(u_t\)
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