Geodesic
On the Inner Radius of a Nodal Domain
Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 249-260

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Let $M$ be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue $\text{ }\!\!\lambda\!\!\text{ }.$ We give upper and lower bounds on the inner radius of the type $C/{{\lambda }^{\alpha }}{{(\log \lambda )}^{\beta }}.$ Our proof is based on a local behavior of eigenfunctions discovered by Donnelly and Fefferman and a Poincaré type inequality proved by Maz’ya. Sharp lower bounds are known only in dimension two. We give an account of this case too.
DOI : 10.4153/CMB-2008-026-2
Mots-clés : 58J50, 35P15, 35P20 
Mangoubi, Dan. On the Inner Radius of a Nodal Domain. Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 249-260. doi: 10.4153/CMB-2008-026-2
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     author = {Mangoubi, Dan},
     title = {On the {Inner} {Radius} of a {Nodal} {Domain}},
     journal = {Canadian mathematical bulletin},
     pages = {249--260},
     year = {2008},
     volume = {51},
     number = {2},
     doi = {10.4153/CMB-2008-026-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-026-2/}
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