Publications

In this article, we consider the time dependent linear elliptic problem with dynamic boundary condition. We recall the corresponding Dirichletto-Neumann operator on Γ denoted by −Λγ. Then we show that when γ = 1 near the boundary, Λγ − Λ1 is bounded by γ − 1 in Lp(Ω) norm. This result is a generalization of the bound with the L∞(Ω) norm and is applicable for comparing the Dirichlet to Neumann semigroup and the Lax semigroup. Finally, we present numerical experiments for validation of our results.