A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions

作者：Bociu Lorena^*; Zolesio Jean Paul

来源：Journal of Differential Equations, 2015, 259(11): 5688-5708.

DOI：10.1016/j.jde.2015.07.006

• Wave equation
• Neumann boundary conditions
• Pseudo-extractor
• Boundary regularity

In this paper we introduce a new approach to "hidden" boundary regularity for the linear wave equation with mixed Dirichlet Neumann boundary conditions, where the Neumann data is non-smooth. First, we obtain existence and uniqueness of solution by Galerkin estimates. Then we use a new, pseudo-extractor technique (based on the Fourier transform and shape and tangential calculus) in order to provide sharp regularity for the solution at the boundary.

• 出版日期2015-12-5