Extended variational formulation (Q2719453)

The author shows how to transform a given problem, linear or nonlinear, into another one that has the same solution and admits a variational formulation with a (true) minimum. For the given problem there exists an infinity of equivalent problems, each with minimality property. The method incorporates the integral transforms whose kernels must satisfy appropriate conditions. A general procedure is described that permits to generate kernels for the initial or boundary value problems with arbitrary domains. The use of degenerate kernels permits to obtain a numerical solution for the problems defined on complicated domains.