Well-Posedness and Regularity for the Wave Equation with Variable Coefficients

In this chapter, we will consider the initial-boundary value problem for the wave equation on a manifold with boundary . The initial-boundary value problem corresponds to the elliptic operator −Δg−Δg introduced in Chap. 2. We will develop a standard approach to prove the existence and uniqueness of solutions and to study their regularity proprieties. © 2017, Springer Science and Business Media Deutschland GmbH. All rights reserved.