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Isoperimetric estimates for the first eigenfunction of a class of linear elliptic problems.
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Isoperimetric estimate for the first eigenfunction of a class of linear elliptic problems
No full textEstimates for solutions to nonlinear degenerate elliptic equations with lower order terms
No full textWe consider a class of Dirichlet boundary problems for nonlinear degenerate elliptic equations with lower order terms. We prove, using symmetrization techniques, pointwise estimates for the rearrangement of the gradient of a solution u and integral estimates. As consequence, we get apriori estimates which show how the summability of the gradient of a solution increases when the summability of the datum increases, also taking into account the presence of a zero order term which can have a regularizing effect
Some properties for eigenvalues and eigenfunctions of a class of linear weighted problems
No full textIsoperimetric estimates for the first eigenfunction of a class of linear elliptic problem
No full textWe 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
Some properties for eigenvalues and eigenfunctions of a class of linear weighted problems
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