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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 3, Pages 404–416 (Mi zvmmf10533)  

On the solvability of some nonlinear elliptic problems

E. V. Golubeva, Yu. A. Dubinskii

National Research University "Moscow Power Engineering Institute"

Abstract: The solvability of second-order nonlinear elliptic equations in weighted Sobolev spaces is analyzed. An additional condition ensuring the solvability of such equations is that the average of the desired solution over some circle of fixed radius is zero. Examples are equations containing a weighted $p$-Laplacian and the Euler equations.

Key words: nonlinear weighted elliptic problems, solvability, average of the solution.

Funding Agency Grant Number
Russian Science Foundation 14-11-00306


DOI: https://doi.org/10.7868/S004446691703005X

Full text: PDF file (209 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:3, 409–421

Bibliographic databases:

UDC: 519.63
Received: 26.07.2016

Citation: E. V. Golubeva, Yu. A. Dubinskii, “On the solvability of some nonlinear elliptic problems”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 404–416; Comput. Math. Math. Phys., 57:3 (2017), 409–421

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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