Results 231 to 240 of about 5,143 (265)

The Dirichlet problem for a Petrovskiî elliptic system of second-order equations

Siberian Mathematical Journal, 1999
The 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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Analyticity of solutions for semilinear elliptic systems of second order

Calculus of Variations and Partial Differential Equations, 2002
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A semilinear second order elliptic system

2011
In this note we consider an equation of the form \[ \begin{cases} \overset{Lu+\beta(u)\ni f(x,u)}{u=0\qquad\qquad} & \overset{in\:\Omega}{su\:\partial\:\Omega}\end{cases} \] where $\Omega\subset\mathbf{R^{\textrm{n}}\textrm{(}}n\geq1)$ is an open set with smooth boundary, L = diag ( L$_{1}$, ...
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The Green Matrix for Strongly Elliptic Systems of Second Order with Continuous Coefficients

Zeitschrift für Analysis und ihre Anwendungen, 1986
We study a generalization of the Green function for elliptic equations to elliptic systems of second order with continuous coefficients. The existence and uniqueness of such a Green matrix as well as various estimates concerning the growth properties near the singular diagonal are proved.
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∂¯‐problem for a second‐order elliptic system in Clifford analysis

Mathematical Methods in the Applied Sciences
In 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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The Dirichlet Problem for an Elliptic System of an Even Number of Second-Order Equations

Differential Equations, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Second Order Elliptic Equations and Elliptic Systems

1998
Ya-Zhe Chen, Lan-Cheng Wu
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Some second-order elliptic systems

Journal of Soviet Mathematics, 1973
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The Lp Dirichlet and regularity problems for second order elliptic systems with application to the Lamé system

Communications in Partial Differential Equations, 2021
Martin Dindoš
exaly  

Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains

Bulletin of Mathematical Sciences, 2011
Vladimir Maz'Ya, Maz'Ya Vladimir
exaly