In this work, we consider the regularized form of the solution of the wave equation and the Poisson equation to provide best possible approximation by the exclusion of singularities. This method enables smoothing solution and allows us to extract some expedient results. To avoid singularities, we use a regularized Green’s function for the Laplace operator in the space  from the theory of reproducing kernel Hilbert space as a strong regularization limit.

regularized Green’s function, regularized solution of partial differential equations, Poisson equation, applications of regularized Green’s function.