A geometric property of level sets of solutions to semilinear elliptic dirichiet problems
- 1 January 1983
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 16 (3) , 229-233
- https://doi.org/10.1080/00036818308839471
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.Keywords
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