A new class of parabolic problems connected with Newton's polygon

Robert Denk; Leonid Volevich

doi:10.3934/proc.2007.2007.294

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2007, Volume 2007: 294-303. Doi: 10.3934/proc.2007.2007.294 open access

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A new class of parabolic problems connected with Newton's polygon

Robert Denk^1, and
Leonid Volevich^2,

1.
Department of Mathematics and Statistics, University of Konstanz, D-78457 Konstanz
2.
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya Square, 125047 Moscow

Received: July 2006

Revised: June 2007

Published: August 2007

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Abstract

A new class of boundary value problems for parabolic operators is introduced. We discuss some linearized free boundary problems not satisfying the classical parabolicity condition. It is shown that they belong to this class and by means of the Newton polygon method the nontrivial two-sided estimates of these problems are found.

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Mathematics Subject Classification: 35K50, 80A22.

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