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EnglishWe find some optimal estimates for the first eigenfunction of a class of elliptic equations whose prototype is - (gamma u(xi)) (xi) = lambda gamma u in Omega subset of R-n with Dirichlet boundary condition, where gamma is the normalized Gaussian function in R-n. To this aim we make use of the Gaussian symmetrization which transforms a domain into an half-space with the same Gaussian measure. The main tools we use are the properties of the weighted rearrangements and in particular the isoperimetric inequality with respect to Gaussian measure.
| Titolo: | Isoperimetric estimates for the first eigenfunction of a class of linear elliptic problem | |
| Autori: | ||
| Data di pubblicazione: | 2007 | |
| Rivista: | ||
| Abstract: | We find some optimal estimates for the first eigenfunction of a class of elliptic equations whose prototype is - (gamma u(xi)) (xi) = lambda gamma u in Omega subset of R-n with Dirichlet boundary condition, where gamma is the normalized Gaussian function in R-n. To this aim we make use of the Gaussian symmetrization which transforms a domain into an half-space with the same Gaussian measure. The main tools we use are the properties of the weighted rearrangements and in particular the isoperimetric inequality with respect to Gaussian measure. | |
| Handle: | http://hdl.handle.net/11367/25162 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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