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Anisotropic adaptive kernel deconvolution

F. ComteC. Lacour — 2013

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we consider a multidimensional convolution model for which we provide adaptive anisotropic kernel estimators of a signal density f measured with additive error. For this, we generalize Fan’s ( (3) (1991) 1257–1272) estimators to multidimensional setting and use a bandwidth selection device in the spirit of Goldenshluger and Lepski’s ( (3) (2011) 1608–1632) proposal for density estimation without noise. We consider first the pointwise setting and then,...

A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources

Gisella CroceCatherine LacourGérard Michaille — 2009

ESAIM: Control, Optimisation and Calculus of Variations

We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order 1 ε concentrated on an ε -neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.

A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources

Gisella CroceCatherine LacourGérard Michaille — 2008

ESAIM: Control, Optimisation and Calculus of Variations

We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order 1 ε concentrated on an -neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.

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