Doubling Property and Vanishing Order of Steklov Eigenfunctions

The paper is concerned with the doubling estimates and vanishing order of the Steklov eigenfunctions on the boundary of a smooth domain in ? ⁿ . The eigenfunction is given by a Dirichlet-to-Neumann map. We improve the doubling property shown by Bellova and Lin. Furthermore, we show that the optimal vanishing order of Steklov eigenfunction is everywhere less than Cλ where λ is the Steklov eigenvalue and C depends only on Ω.