Klyachin A.A. The variational equality for the functional of the general form

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http://dx.doi.org/10.15688/jvolsu1.2012.2.4

 

Klyachin Alexey Alexandrovich
 
Doctor of Physics and Mathematics, Head of Chair of Mathematical Analysis and Function Theory, Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. We defined a characteristic that serves as a measure of the difference of two vectors associated with a convex function. In terms of this characteristic we establish the variational equality for the extremals of the functional of general form. We consider the results for the minimal surface equation in Finsler space and give them a geometric interpretation. Corollary of results is the convergence “on average” sequence that minimizes this functional.

Key words: variational problem, minimization of a convex functional, the minimal surface equation, mixed boundary value problem, Finsler metric.

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The variational equality for the functional of the general form by Klyachin A.A. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (17) 2012 pp. 18-29

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