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Gradient estimates for degenerate diffusion equations II†

Published online by Cambridge University Press:  14 November 2011

Nicholas D. Alikakos  and
Rouben Rostamian
Nicholas D. Alikakos
Affiliation:
Mathematics Department, Purdue University, West Lafayette, Indiana 47907, U.S.A.
Rouben Rostamian
Affiliation:
Mathematics Department, Purdue University, West Lafayette, Indiana 47907, U.S.A.
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Synopsis

We establish upper and lower bounds for various norms of solutions and their gradients for the equation ut = div (|∇u|m−1 ∇u) in ℝN in terms of the norms of the initial data. Based on the L∞ estimate of ∇u, we conclude that u(x, t) is Lipschitz continuous in space-time, for all t>0, whenever u(x,0) is in L1(ℝN).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 3-4 , 1982 , pp. 335 - 346
Copyright
Copyright © Royal Society of Edinburgh 1982

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