On a New Generalization of the Lax-Milgram Lemma

We consider a new generalization of the celebrated Lax-Milgram Lemma, which is called the harmonic Lax-Milgram Lemma. Some special cases are discussed. New concepts are introduced. The auxiliary principle approach is applied to discuss the existence of the solution as well as to propose some iterative schemes for computing the approximate solution of harmonic Max-Milgram Lemma. Convergence analysis of the proposed methods is considered under some mild conditions. Ideas and techniques of this paper may stimulate further research.