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On the absence of global solutions to the gauss equation and solutions in external areas

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Abstract

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 to the second-order elliptic equation with variable coefficients in its linear part.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Rubtsovskaya nab. 2/18, Moscow, 105005, Russia

    A. V. Neklyudov

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  1. A. V. Neklyudov
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Correspondence to A. V. Neklyudov.

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Original Russian Text © A.V. Neklyudov, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 1, pp. 55–60.

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Neklyudov, A.V. On the absence of global solutions to the gauss equation and solutions in external areas. Russ Math. 58, 47–51 (2014). https://doi.org/10.3103/S1066369X14010058

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  • DOI: https://doi.org/10.3103/S1066369X14010058

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