Integral Property of Laplace Operator

Relations have been derived which establish connection between a scalar or a vector functions and the integral of Laplace operator of these functions (the integral property of Laplace operator). The integral property of Laplace operator was employed to obtain relations expressing the electric field in terms of the charge gradient. It is demonstrated that these relations define the same field which is described by the well known classical expressions for the electric field. It is shown that these proposed expressions represent actually a particular case of the general theory of generalized functions. This approach is illustrated by calculation of an electric field performed with the proposed formalism.