数学物理边值问题的双场拉格朗日乘子弱解

IF 1.6 3区数学 Q1 MATHEMATICS

Mathematical Modelling and Analysis Pub Date : 2022-11-10 DOI:10.3846/mma.2022.15827

Mariana Chivu Cojocaru, A. Matei

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引用次数: 1

摘要

提出了求解数学物理边值问题的一种新的变分方法。通过考虑双场拉格朗日乘子，我们给出了一个由混合变分问题组成的变分公式，该变分问题等价于鞍点问题。因此，我们提出的弱公式的唯一可解性是由鞍点理论控制的。本文还讨论了几种不同的变分公式及其联系。

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Weak solutions via two-field Lagrange Multipliers for boundary Value Problems in Mathematical Physics

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.

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