In this paper we provide some bounds for the eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of R^n. 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.
Sharp estimates for eigenfunctions of a Neumann problem / Brandolini, Barbara; Chiacchio, Francesco; Trombetti, Cristina. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 34:(2009), pp. 1317-1337. [10.1080/03605300903089859]
Sharp estimates for eigenfunctions of a Neumann problem
BRANDOLINI, BARBARA;CHIACCHIO, FRANCESCO;TROMBETTI, CRISTINA
2009
Abstract
In this paper we provide some bounds for the eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of R^n. 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.File in questo prodotto:
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