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.

Isoperimetric estimates for the first eigenfunction of a class of linear elliptic problem

Betta, M. F.;
2007

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/25162
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