Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physics

Abstract

A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle point problem. Thus, the unique solvability of the weak formulation we propose is governed by the saddle point theory. Alternative variational formulations and some of their connections are also discussed.

Keywords

• partial differential equations
• subdifferential inclusions
• two-field Lagrange multipliers
• weak solutions
• saddle points