Geodesic
On the absence of global solutions of the Gauss equation and solutions in external areas
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2014), pp. 55-60

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We consider conditions under which the Gauss equation has no solutions defined in the whole space or in areas external with respect to a ball. The absence of solutions in external areas is established in the case when the number of independent variables is more than two. In the two-dimensional case we obtain conditions ensuring the absence of global solutions of the second-order elliptic equation with variable coefficients in its linear part.
Mots-clés : Gauss equation, absence of global solutions, absence of solutions in exterior domains. 
@article{IVM_2014_1_a4,
     author = {A. V. Neklyudov},
     title = {On the absence of global solutions of the {Gauss} equation and solutions in external areas},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {55--60},
     publisher = {mathdoc},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_1_a4/}
}
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A. V. Neklyudov. On the absence of global solutions of the Gauss equation and solutions in external areas. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2014), pp. 55-60. http://geodesic.mathdoc.fr/item/IVM_2014_1_a4/