Elimination of Hamilton-Jacobi equation in extreme variational problems

2010/08/16 by I. V. Orlov, Igor Orlov, Orlov, Igor
Computer Science · Mathematics · #49J05 #49L99 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #G.1.6 #G.1.8 #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #acm:49J05 #acm:49L99 #math.AP #math.FA #math.OC #msc:49J05 #msc:49L99

paper · pdf · doi:10.48550/arxiv.1008.2599

10 pages

arxiv created 2010/08/16 · openalex publication_date 2010/08/16 · arxiv updated 2010/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that extreme problem for one-dimensional Euler-Lagrange variational functional in C¹[a;b] under the strengthened Legendre condition can be solved without using Hamilton-Jacobi equation. In this case, exactly one of the two possible cases requires a restriction to a length of [a;b], defined only by the form of integrand. The result is extended to the case of compact extremum in H¹[a;b].

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