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This article is cited in 1 scientific paper (total in 1 paper)
Boundedness of solutions to anisotropic second order elliptic equations in unbounded domains
L. M. Kozhevnikova, A. A. Khadzhi Sterlitamak branch of Bashkir State University, Sterlitamak, Russia
Abstract:
In the paper we study a class of anisotropic second order elliptic equations represented by the model equation
$$
\sum_{\alpha=1}^n(|u_{x_\alpha}|^{p_\alpha-2}u_{x_\alpha})_{x_\alpha}=\sum_{\alpha=1}^n\left(\Phi_\alpha(\mathbf x)\right)_{x_\alpha},\quad p_n\geq\ldots\geq p_1>1.
$$
We prove the boundedness of solutions to the homogeneous Dirichlet problem in unbounded domains located along one of the coordinate axes. We also establish an estimate for the solutions to the considered equations with a compactly supported right hand side that ensures a power decay of the solutions at infinity.
Keywords:
Dirichlet problem, anisotropic elliptic equation, unbounded domain, boundedness of solutions, decay of solution.
Received: 05.11.2013
Citation:
L. M. Kozhevnikova, A. A. Khadzhi, “Boundedness of solutions to anisotropic second order elliptic equations in unbounded domains”, Ufimsk. Mat. Zh., 6:2 (2014), 67–77; Ufa Math. J., 6:2 (2014), 66–76
Linking options:
https://www.mathnet.ru/eng/ufa244https://doi.org/10.13108/2014-6-2-66 https://www.mathnet.ru/eng/ufa/v6/i2/p67
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Abstract page: | 310 | Russian version PDF: | 137 | English version PDF: | 6 | References: | 49 |
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