In this paper we provide some bounds for eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of Rn. To this aim we use the so-called symmetrization techniques and the obtained estimates are asymptotically sharp, at least in the bidimensional case, when the isoperimetric constant relative to Ω goes to 0.
Brandolini B., Chiacchio F., Trombetti C. (2009). Sharp estimates for eigenfunctions of a Neumann problem. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 34(11), 1317-1337 [10.1080/03605300903089859].
Sharp estimates for eigenfunctions of a Neumann problem
Brandolini B.;
2009-01-01
Abstract
In this paper we provide some bounds for eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of Rn. To this aim we use the so-called symmetrization techniques and the obtained estimates are asymptotically sharp, at least in the bidimensional case, when the isoperimetric constant relative to Ω goes to 0.
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