Analysis of the existence of special solutions to the capillarity problem
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 113-118.

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This paper is devoted to the study of the existence of solutions of the capillary equation under the influence of an external potential leading to surface surgery.
Keywords: capillarity problem, Bond number, special solution.
Mots-clés : bifurcation
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L. V. Stenyukhin. Analysis of the existence of special solutions to the capillarity problem. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 113-118. http://geodesic.mathdoc.fr/item/INTO_2019_172_a8/

[1] Borisovich A. Yu., “Operator Plato i bifurkatsii dvumernykh minimalnykh poverkhnostei”, Globalnyi analiz i matematicheskaya fizika, Voronezh, 1987, 142–155

[2] Dao Chong Tkhi, Fomenko A. T., Minimalnye poverkhnosti i problema Plato, Nauka, M., 1987 | MR

[3] Darinskii B. M., Sapronov Yu. I., Tsarev S. L., “Bifurkatsii ekstremalei fredgolmovykh funktsionalov”, Sovr. mat. Fundam. napravl., 12 (2004), 3–140 | Zbl

[4] Nirenberg L., Lektsii po nelineinomu funktsionalnomu analizu, Mir, M., 1987

[5] Stenyukhin L. V., “O minimalnykh poverkhnostyakh s ogranicheniyami tipa neravenstv”, Izv. vuzov. Mat., 11 (2012), 51–59 | MR | Zbl

[6] Stenyukhin L. V., “Ob osobykh resheniyakh zadachi kapillyarnosti s krugovoi simmetriei”, Vestn. Voronezh. gos. un-ta. Ser. Fiz. Mat., 2 (2013), 242–245

[7] Stenyukhin L. V., “Bifurkatsionnyi analiz zadachi kapillyarnosti s krugovoi simmetriei”, Vestn. Yuzhno-Ural. gos. un-ta. Ser. Mat. model. program., 7:2 (2014), 77–83 | Zbl

[8] Uraltseva N. N., “Reshenie zadachi kapillyarnosti”, Vestn. LGU, 19 (1973), 54–64 | Zbl

[9] Finn R., Ravnovesnye kapillyarnye poverkhnosti. Matematicheskaya teoriya, Mir, M., 1989

[10] Wente H. C., “The symmetry of sessile and pendent drops”, Pac. J. Math., 88:2 (1980), 387–397 | DOI | MR | Zbl