Existence of Solutions for the Evolution ð ‘ ( ð ‘¥ ) -Laplacian Equation Not in Divergence Form

Changchun Liu, Junchao Gao and Songzhe Lian

Journal of Applied Mathematics, 2012, vol. 2012, 1-21

Abstract:

The existence of weak solutions is studied to the initial Dirichlet problem of the equation ð ‘¢ ð ‘¡ = ð ‘¢ d i v ( | ∇ ð ‘¢ | ð ‘ ( ð ‘¥ ) − 2 ∇ ð ‘¢ ) , with inf ð ‘ ( ð ‘¥ ) > 2 . We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:835495

DOI: 10.1155/2012/835495

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