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Applicable Analysis
An International Journal
Volume 16, 1983 - Issue 3
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Original Articles

A geometric property of level sets of solutions to semilinear elliptic dirichiet problems

Bernhard Kawohl Division of Applied Mathematics, Brown University, Providence, R.I, 02912, U.S.A; Institut für Angewander Mathematik, Universität Erlangen, Erlangen, 8520, West-Germany
Pages 229-233 | Published online: 10 May 2007
 
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Abstract

It is shown that under certain geometrical assumptions on a domain any positive solution of △u+f(u)=0 in D, u=0 on ∂D has level Sets with the same geometrical properties as D. This implies that u has only one critical point and externds results of PAYNE1 and SPERß2.

AMS(MOS)Classification Numbers:

†This research was supported in part by the Deutsche Forschunesemeinschaft.

†This research was supported in part by the Deutsche Forschunesemeinschaft.

Notes

†This research was supported in part by the Deutsche Forschunesemeinschaft.

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