Boundary-value problems for the wave equation with Lévy Laplacian in the Gâteaux class - Feller, M. N. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
We present the solutions of the initial-value problem in the entire space and the solutions of the boundary-value and initial-boundary-value problems for the wave equation ∂^2U(t,x)∂x^2 = Δ_LU(t,x) with infinite-dimensional Lévy Laplacian Δ_L in the class of Gâteaux functions.