Free transmission problems

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.

Paper from Marcelo Amaral's thesis, distinguished at the 2015 Carlos Gutierrez prize for best thesis

References in corpus (2)

• Gradient estimates for parabolic and elliptic systems from linear laminates
• Interior Regularity Estimates in High Conductivity Homogenization and Application

Cited by in corpus (1)

• A proof of the $C^{p^{\prime }}$-regularity conjecture in the plane