On the use of direct variational methods in applications

Ternovskii, V. V.; Khapaev, M. M.
February 2011
Doklady Mathematics;Feb2011, Vol. 83 Issue 1, p113
Academic Journal
The article discusses the use of direct variational methods in mathematical applications. It notes the necessity of functional analysis, topology, and computational mathematics for solving problems in the fields of mechanics, physics, and economics. The analytical methods for functional minimization are lessened to solve the Euler differential equation. It points out that variational approach is commonly used in finding solutions to the theory of ill-posed inverse problems. It explains the artificial increase in solution smoothness and a priori information loss which is caused by the transition to the Euler equation in ill-posed problems.


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