Abstract
We consider a bounded open subset 𝕀 o of ℝ n with 0 ∈ 𝕀 o , and a function f o of ∂𝕀 o to ℝ. Under reasonable assumptions, the Dirichlet problem Δu = 0 in 𝕀 o , u = f o on ∂𝕀 o , has one and only one solution ũ o . Then we consider another bounded open subset 𝕀 i of ℝ n with 0 ∈ 𝕀 i , and an increasing diffeomorphism F of ℝ onto itself, and a constant γ ∈]0, +∞[, and a function g of ∂𝕀 i to ℝ, and we consider the non-linear transmission boundary value problem
Acknowledgement
The author is indebted to V.V. Mityushev and S.V. Rogosin for several discussions on transmission problems in the frame of the applications, and for pointing out to the author problem (Equation2).