A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions
An IBV problem for the linear inhomogeneous wave equation with mixed (Dirichlet and Neumann) boundary conditions is analyzed. Actually, one considers a zero Dirichlet boundary condition on a part of the boundary and a non-smooth Neumann boundary condition on the remainder of the boundary of the domain. Under a special assumption on interior and boundary data, the existence, uniqueness and interior regularity of solution is proved. For the proof, standard Galerkin approximation technique is used. Under additional assumptions on interior and boundary data, hidden boundary regularity for the solution of the wave equation is proved. For the proof, one introduces the so called pseudo-extractor technique which makes use of the Fourier transform and shape optimization techniques.
scientific article; zbMATH DE number 6484221
scientific article