# American Institute of Mathematical Sciences

2007, 2007(Special): 294-303. doi: 10.3934/proc.2007.2007.294

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

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

Received  July 2006 Revised  June 2007 Published  September 2007

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.
Citation: Robert Denk, Leonid Volevich. A new class of parabolic problems connected with Newton's polygon. Conference Publications, 2007, 2007 (Special) : 294-303. doi: 10.3934/proc.2007.2007.294
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