Geodesic
Inverse extremal problem for variational functionals
Eurasian mathematical journal, Tome 1 (2010) no. 4, pp. 95-115 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate an inverse extremal problem for the variational functionals: to describe, under certain conditions, all types of variational functionals having a local extremum (in case of the space $C^1[a;b]$) or a compact extremum (in case of the Sobolev space $W^{1,2}[a;b]=H^1[a;b]$) at a given point of the corresponding function space. The non-locality conditions for a compact extrema of variational functionals are described as well. 
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I. V. Orlov. Inverse extremal problem for variational functionals. Eurasian mathematical journal, Tome 1 (2010) no. 4, pp. 95-115. http://geodesic.mathdoc.fr/item/EMJ_2010_1_4_a4/

[1] E. V. Bozhonok, “On solutions to “almost everywhere” – Euler–Lagrange equation in Sobolev space $H^1$”, Methods of Funct. Anal. and Top., 13:3 (2007), 262–266 | MR | Zbl

[2] E. V. Bozhonok, “Some existence conditions of compact extrema for variational functionals of several variables in Sobolev space $H^1$”, Operator Theory Adv. and Appl., 190 (2009), 41–155 | MR

[3] E. V. Bozhonok, I. V. Orlov, “Legendre and Jacobi conditions of compact extrema for variation functionals in Sobolev spaces”, Pratsi Inst. Matem. Nats. Akad. Nauk Ukr., 3:4 (2006), 282–293 (Russian)

[4] B. Dacorogna, Introduction to the calculus of variations, Imperial College Press, London, 2004 | MR

[5] M. Giaquinta, S. Hildebrandt, Calculus of Varitions, Springer, New York, 1996 | Zbl

[6] I. V. Orlov, “Compact extrema: general theory and its applications to the variational functionals”, Operator Theory Adv. and Appl., 190 (2009), 397–417 | MR | Zbl

[7] I. V. Orlov, E. V. Bozhonok, “Conditions of existence, $K$-continuity and $K$-differentiability of Euler–Lagrange functional in Sobolev space $W_2^1$”, Uchenye Zapiski Tavricheskogo Natsynal'nogo Universiteta, 19:2 (2006), 63–78 (Russian)

[8] I. Orlov, Elimination of Hamilton–Jacobi equation in extreme variational problems, 10 pp., arXiv: 1008.2599 | MR

[9] I. V. Orlov, “Extreme Problems and Scales of the Operator Spaces”, North–Holland Math. Studies. Funct. Anal and Appl., 197 (2004), 209–228 | DOI | MR

[10] I. V. Orlov, “$K$-differentiability and $K$-extrema”, Ukrainskii Matem. Vestnik, 3:1 (2006), 97–115 (Russian) | MR | Zbl

[11] I. V. Orlov, “Normal differentiability and extrema of functionals in locally convex space”, Kibernetika i Sistemnyi Analiz, 2002, no. 4, 24–35 (Russian) | MR | Zbl

[12] E. A. M. Rocha, D. F. M. Torres, “First integrals for problems of calculus of variations on locally convex spaces”, Applied Sciences, 10 (2008), 207–218 | MR | Zbl

[13] H.-J. Schmeisser, W. Sickel, “Spaces of functions of mixed smoothness and approximation from hyperbolic crosses”, J. Approx. Theory, 128:2 (2004), 115–150 | DOI | MR | Zbl

[14] I. V. Skrypnik, Nonlinear elliptic high order equations, Naukova Dumka, Kiev, 1973 (Russian)

[15] H. Triebel, Theory of Function Spaces, v. III, Monographs in Math., 100, Birkhäuser, Basel, 2006 | MR | Zbl