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arXiv · 1510.01263

Free transmission problems

Marcelo Amaral·Eduardo V. Teixeira
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Abstract

We study transmission problems with free interfaces from one random medium to another. Solutions are required to solve distinct partial differential equations, $\mbox{L}_{+}$ and $\mbox{L}_{-}$, within their positive and negative sets respectively. A corresponding flux balance from one phase to another is also imposed. We establish existence and $L^{\infty}$ bounds of solutions. We also prove that variational solutions are non-degenerate and develop the regularity theory for solutions of such free boundary problems.

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Marcelo Amaral, Eduardo V. Teixeira. 2015-10-05. Free transmission problems. https://doi.org/10.1007/s00220-015-2290-3

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