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$$\frac{∂^2U(t,x)}{∂x^2} = Δ_LU(t,x)$$with infinite-dimensional Lévy Laplacian $Δ_L$ in the class of Gâteaux functions.