Displaying similar documents to “Sets with prescribed lower and upper weighted densities.”

On relations between f -density and ( R ) -density

Václav Kijonka (2007)

Acta Mathematica Universitatis Ostraviensis

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In this paper it is discus a relation between f -density and ( R ) -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.

Isoperimetric and Stable Sets for Log-Concave Perturbations of Gaussian Measures

César Rosales (2014)

Analysis and Geometry in Metric Spaces

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Let be an open half-space or slab in ℝn+1 endowed with a perturbation of the Gaussian measure of the form f (p) := exp(ω(p) − c|p|2), where c > 0 and ω is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to ∂ Ω. In this work we follow a variational approach to show that half-spaces perpendicular to ∂ Ω uniquely minimize the weighted perimeter in Ω among sets enclosing the same weighted volume. The main ingredient of the proof is the...

General Gagliardo Inequality and Applications to Weighted Sobolev Spaces

Antonio Avantaggiati, Paola Loreti (2009)

Bollettino dell'Unione Matematica Italiana

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In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].