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The Dirichlet problem for a Petrovskiî elliptic system of second-order equations
Siberian Mathematical Journal, 1999The apparatus of singular integral equations is applied to studying the Dirichlet problem for the system \[ -\Delta u_j + \lambda_j\frac{\partial}{\partial x_j}\sum_{i=1}^n \frac{\partial u_i}{\partial x_i} = 0,\qquad j=1,\dots, n. \] The main results of the article are as follows: Theorem 1. If the parameters \(\lambda_j\) of the system satisfy either
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∂¯‐problem for a second‐order elliptic system in Clifford analysis
Mathematical Methods in the Applied SciencesIn the framework of Clifford analysis, we study a second‐order elliptic (generally nonstrongly elliptic) system of partial differential equations of the form: , where stands for the Dirac operator with respect to a structural set . The solutions of this system are known as ‐inframonogenic functions.
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Second Order Elliptic Equations and Elliptic Systems
1998Ya-Zhe Chen, Lan-Cheng Wu
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Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis, 2002Douglas N Arnold +2 more
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Weak Galerkin methods for second order elliptic interface problems
Journal of Computational Physics, 2013Lin Mu, Xiu Ye, Shan Zhao
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A weak Galerkin mixed finite element method for second order elliptic problems
Mathematics of Computation, 2014Xiu Ye
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