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Marcelo Amaral (Unilab-Brazil)

Transmission problems on free interfaces

We study transmission problems with free interfaces from one random medium to another. Solutions are required to solve distinct partial differential equations, L + and 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 infinity bounds of solutions. We also prove that variational solutions are non-degenerate and develop the regularity theory for solutions of such free boundary problems.