Shape derivative for the Dirichlet-to-Neumann operator on a manifold and application to cellular protrusion

We establish a shape-derivative formula for the Dirichlet-to-Neumann operator on a compact manifold. Then, we apply this formula to obtain the well-posedness in H 1 under a specific Rayleigh-Taylor condition to an equation describing cell protrusions. This equation is a generalisation of the theoretical part of [9] to any -2D as well as 3D-surfaces.