Gilles Evequoz: Real-valued L^p-solutions of the nonlinear Helmholtz equation

The Helmholtz equation appears as a model for the propagation of acoustic waves. Starting from the linear theory, which will be briefly reviewed, we will present new results obtained using variational methods and concerning the existence and the far field expansion of real-valued L^p solutions in the nonlinear case. These solutions correspond to time-periodic solutions of the corresponding wave equation having constant energy density (standing waves). The talk is based on a joint work with Tobias Weth.