Geodesic
Some Properties of Extremals of the Functional of Potential Energy
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 103-109

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In this paper, we discuss stability and instability criteria for extremal surfaces of a special functional, which is a linear combination of an area-type functional and the functional of volumetric force density. Extremals of such functionals can serve as models of physically equilibrium tents or liquids in potential gravitational fields, so that the problem of their stability or instability is very topical. Our results are based on various geometric properties of surfaces; they are obtained by methods developed by V. M. Miklyukov and V. A. Klyachin.
Keywords: variation of functional, extremal surface, extremal of surface, area-type functional, functional of volumetric force density, functional of potential energy, stability, instability, base frequency.
Mots-clés : Jacobi equation 
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     author = {N. M. Poluboyarova},
     title = {Some {Properties} of {Extremals} of the {Functional} of {Potential} {Energy}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {103--109},
     publisher = {mathdoc},
     volume = {152},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2018_152_a8/}
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N. M. Poluboyarova. Some Properties of Extremals of the Functional of Potential Energy. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 103-109. http://geodesic.mathdoc.fr/item/INTO_2018_152_a8/