Representation of functions as the Post-Widder inversion operator of generalized functions.

Manandhar, R.P.; Debnath, L.

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We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, ${\nabla u_{k}}$ , bounded in $L^{p} (Ø; ℝ^{m \times n})$ if $p > 1$ and $Ω \subset ℝ^{n}$ 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 $Ω$ are required and links with lower semicontinuity...

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