Monotonicity results for the principal eigenvalue of the generalized Robin problem
Giorgi, Tiziana ; Smits, Robert G.
Illinois J. Math., Tome 49 (2005) no. 2, p. 1133-1143 / Harvested from Project Euclid
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We study domain monotonicity of the principal eigenvalue $\lambda_1^\Omega(\alpha)$ corresponding to $\Delta u=\lambda(\alpha) \, u \text{ in } \Omega, \frac{\partial u}{\partial \nu} =\alpha\, u \text{ on } \partial \Omega$, with $\Omega \subset {\mathcal R}^n$ a $C^{0,1}$ bounded domain, and $\alpha$ a fixed real. We show that contrary to intuition domain monotonicity might hold if one of the two domains is a ball.
Publié le : 2005-10-15
Classification:  35P15,  35J25 
@article{1258138130,
     author = {Giorgi, Tiziana and Smits, Robert G.},
     title = {Monotonicity results for the principal eigenvalue of the generalized Robin problem},
     journal = {Illinois J. Math.},
     volume = {49},
     number = {2},
     year = {2005},
     pages = { 1133-1143},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138130}
}

Giorgi, Tiziana; Smits, Robert G. Monotonicity results for the principal eigenvalue of the generalized Robin problem. Illinois J. Math., Tome 49 (2005) no. 2, pp.  1133-1143. http://gdmltest.u-ga.fr/item/1258138130/