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Flat core properties associated to the $ p$-Laplace operator

Authors: Shoshana Kamin and Laurent Véron
Journal: Proc. Amer. Math. Soc. 118 (1993), 1079-1085
MSC: Primary 35J60; Secondary 35J70
MathSciNet review: 1139470
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Abstract: We study the formation of a flat hat pattern in the profile of the positive solution of an equation of the type: $ \varepsilon {\Delta _p}u - {u^{p - 1}}{(1 - u)^\theta } = 0\;(0 < \theta < p - 1)$ in a bounded domain $ \Omega $. When $ \varepsilon $ tends to $ {0^ + }$, the growth of the zone where $ u = {u_\varepsilon }$ takes the value $ 1$ in $ \Omega $ is studied.

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Article copyright: © Copyright 1993 American Mathematical Society

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