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This article is cited in 13 scientific papers (total in 13 papers)
Removability of an isolated singularity for anisotropic elliptic equations with absorption
I. I. Skrypnik Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
Abstract:
This paper is concerned with the investigation of solutions with a point singularity of the general elliptic equation
$$
-\sum_{i=1}^n\frac\partial{\partial x_i}
\biggl(\biggl|\frac{\partial u}{\partial x_i}\biggr|^{p_i-2}\frac{\partial u}{\partial x_i}\biggr)+|u|^{q-1}u=0.
$$
A method for deriving new pointwise estimates for the solution and integral estimates for the gradient of the solution is developed. Precise conditions are established on the behaviour of the term characterizing the absorption to ensure the non-existence of solutions with a point singularity.
Bibliography: 11 titles.
Received: 14.06.2007 and 25.11.2007
Citation:
I. I. Skrypnik, “Removability of an isolated singularity for anisotropic elliptic equations with absorption”, Mat. Sb., 199:7 (2008), 85–102; Sb. Math., 199:7 (2008), 1033–1050
Linking options:
https://www.mathnet.ru/eng/sm3909https://doi.org/10.1070/SM2008v199n07ABEH003952 https://www.mathnet.ru/eng/sm/v199/i7/p85
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Abstract page: | 442 | Russian version PDF: | 199 | English version PDF: | 11 | References: | 56 | First page: | 9 |
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