| Abstract: |
| In this talk, we shall discuss a homogenization problem with nonlinear boundary conditions.
Main results consist of a homogenization theorem without assumptions for the periodicity of the oscillating coefficient, i.e., convergence of solutions as the oscillating parameter of coefficients goes to zero and characterization of the homogenized equation and an existence theorem for optimal two-phase domains that minimize energies constructed by solutions of elliptic equations with nonlinear boundary conditions. Furthermore, we shall discuss such domains by employing a level set method based on nonlinear diffusion. |
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