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

Gisella Croce; Catherine Lacour; Gérard 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 $\frac{1}{\sqrt{ε}}$ 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 Croce; Catherine Lacour; Gérard 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 $\frac{1}{\sqrt{ε}}$ 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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