On the square root of a Laplace-Beltrami operator

Abstract: A central part of the study of free boundary problems is related to the properties of the Dirichlet to Neumann operator (DNO). In particular, it is known that DNO is related to the Beltrami-Laplace operator associated with the surface. An important application of this observation was given in the celebrated paper by Lannes published in the Journal of the AMS in 2005, where he proved the well-posedness of the water waves equations. 

In this talk, I will present this key observation that relates the DNO with the square root of the Laplace-Beltrami operator.