Displaying similar documents to “A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources”

The nonlinear membrane model: a Young measure and varifold formulation

Med Lamine Leghmizi, Christian Licht, Gérard Michaille (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We establish two new formulations of the membrane problem by working in the space of W Γ 0 1 , p ( Ω , 𝐑 3 ) -Young measures and W Γ 0 1 , p ( Ω , 𝐑 3 ) -varifolds. The energy functional related to these formulations is obtained as a limit of the formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing...

Links between Young measures associated to constrained sequences

Anca-Maria Toader (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We give necessary and sufficient conditions which characterize the Young measures associated to two oscillating sequences of functions, on ω 1 × ω 2 and on ω 2 satisfying the constraint v n ( y ) = 1 | ω 1 | ω 1 u n ( x , y ) d x . Our study is motivated by nonlinear effects induced by homogenization. Techniques based on equimeasurability and rearrangements are employed.

Oscillations and concentrations in sequences of gradients

Agnieszka Kałamajska, Martin Kružík (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We use DiPerna's and Majda's generalization of Young measures to describe oscillations and concentrations in sequences of gradients, { u k } , bounded in L p ( Ω ; m × n ) if and Ω n is a bounded domain with the extension property in W 1 , p . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of are required and links with lower semicontinuity...