Results 221 to 230 of about 5,143 (265)

Non variational basic elliptic systems of second order

Rendiconti del Seminario Matematico e Fisico di Milano, 1990
The author considers fully nonlinear nonvariational elliptic systems of the type \[ a(H(u))=f \quad \text{in }\Omega \subset \mathbb{R}^ n, \tag{1} \] where \(u:\Omega \to \mathbb{R}^ N\) is vector valued, and \(H(u):=\{D_ iD_ ju\}\) \((i,j=1,\dots,n)\) is the matrix of the second partial derivatives of \(u\).
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The Cauchy Problem for Second-Order Elliptic Systems on the Plane

Siberian Mathematical Journal, 2003
The author gives a representation in \(A\)-analytic functions of solutions to the second-order elliptic system with constant coefficients and two independent variables \[ {\mathcal A} \frac{\partial^2}{\partial x^2} V +2 {\mathcal B} {\partial^2 \over \partial x \partial y} V + {\mathcal C} {\partial^2 \over \partial y^2} V = 0.
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Twice Periodic Solutions of a Nonlinear Elliptic Second-Order Systems

Lobachevskii Journal of Mathematics, 2018
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Safarov, D. S., Shodiev, M. S.
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On the complex spectra of second order elliptic systems

Results in Mathematics, 1989
The author studies the complex spectra of second order elliptic systems \[ Lu\equiv -A_{ij}(x)u_{,ij}+B_ i(x),u_{,i}+C(x)u=\lambda M(x)u\quad in\quad \Omega,\quad u=0\quad on\quad \partial \Omega, \] \(\Omega \subset {\mathbb{R}}^ n\) a bounded \(C^{2+\theta}\)-domain, \(A_{ij}\), \(B_ i\), C, M are \(N\times N\)-matrices, \(A_{ij}\) satisfies \(Re a^{\
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On a weak extremum principle for a second-order elliptic system

Izvestiya: Mathematics, 1995
Summary: A class of second-order elliptic systems is discussed, for which a notion of `stochastic' weak extremum principle is introduced, and some necessary and sufficient conditions for it to hold are proved.
Kamynin, L. I., Khimchenko, B. N.
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Second-order elliptic systems in the half-plane

Izvestiya: Mathematics, 2006
We consider boundary-value problems in the upper half-plane for second-order elliptic systems with constant higher coefficients. Using the Bitsadze transformation, we reduce these problems to equivalent problems for analytic functions. This approach enables us to obtain explicit formulae for the solutions of basic boundary-value problems and to study ...
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Integral Representations for Second-Order Elliptic Systems in the Plane

Computational Mathematics and Mathematical Physics
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On a class of Second Order Elliptic Overdetermined Systems

1999
Some second order complex overdetermined systems of partial differential equations in the unit ball of ℂ n or in the whole space ℂ n , n ≥ 1, are studied. The systems are regular or singular. For inhomogeneous systems the compatibility and solvability conditions are derived and for the homogeneous systems the structure of their solutions are ...
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Second-Order Elliptic Systems with Periodic Coefficients

2018
In this monograph we shall be concerned with a family of second-order linear elliptic operators in divergence form with rapidly oscillating periodic coefficients, $$\mathcal{L}_\varepsilon = - \mathrm{div}(\mathit{A}(\mathit{x}/\varepsilon)\nabla), \,\,\, \varepsilon > 0,$$ (2.0.1) in \(\mathbb{R}^\mathit{d}\). The coefficient matrix (tensor)
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Generalized Poisson Formula for Second Order Elliptic Systems

Journal of Mathematical Sciences
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