Young measure minimizers in the asymptotic analysis of thin films



Marian Bocea
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213 U.S.A.
mbocea@andrew.cmu.edu

Abstract: An integral representation for a relaxed functional arising in the membrane theory is obtained in terms of Young measures generated by sequences $\left\{ \left( \nabla _{\alpha}u_{\varepsilon _n } \big\vert \frac{1}{\varepsilon_n }\nabla _3 u_{\varepsilon _n} \right) \right\} $ of scaled gradients.

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