Results 241 to 250 of about 142,024 (284)

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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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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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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Generalized Poisson Formula for Second Order Elliptic Systems

Journal of Mathematical Sciences
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Finite element methods for nonlinear elliptic systems of second order

Mathematische Nachrichten, 1980
AbstractThis paper deals with the finite element displacement method for approximating isolated solutions of general quasilinear elliptic systems. Under minimal assumptions on the structure of the continuous problems it is shown that the discrete analogues also have locally unique solutions which converge with quasi‐optimal rates in L2 and L∞.
Dobrowolski, Manfred, Rannacher, Rolf
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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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Integral Representations for Second-Order Elliptic Systems in the Plane

Computational Mathematics and Mathematical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Hybrid coupled finite–boundary element methods for elliptic systems of second order

Computer Methods in Applied Mechanics and Engineering, 2000
The authors design a hybrid method which combines the global characterization of the stress field with locally high resolution in chosen subdomains. It is meant to be able to handle particular situations involving singular features such as cracks, inclusions, corners or notches.
Hsiao, George C., Schnack, Eckart, Wendland, Wolfgang L.   +2 more
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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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