Geodesic
Variational problem of the two-phase medium elasticity theory for the zero surface tension coefficient
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 208-225

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In this article, we give a proof of the existence theorem for an equilibrium state for the surface tension coefficient $\sigma=0$ and investigate the behavior of the equilibrium state for small $\sigma$. Bibliography: 4 titles. 
@article{ZNSL_1995_221_a12,
     author = {V. G. Osmolovski},
     title = {Variational problem of the two-phase medium elasticity theory for the zero surface tension coefficient},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {208--225},
     publisher = {mathdoc},
     volume = {221},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a12/}
}
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V. G. Osmolovski. Variational problem of the two-phase medium elasticity theory for the zero surface tension coefficient. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 208-225. http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a12/