The generalized spectrum of second order elliptic systems

On the Generalized Spectrum for Second-order Elliptic Systems

We consider the system of homogeneous Dirichlet boundary value problems (*) Liu = A[an(x)u + a\2(x)v], L2V = ti[ai2{x)u + a.22{x)v] in a smooth bounded domain fi C R", where Li and £2 are formally selfadjoint second-order strongly uniformly elliptic operators. Using linear perturbation theory, continuation methods, and the Courant-Hilbert variational eigenvalue characterization, we give a detai...

Generalized Second-order Two-dimensional Systems: Computing the Transfer Function

In this paper the discrete Fourier transform is used to determine the coefficients of a transfer function of a new twodimensional model of second-order: x(i1 +2, i2 +2) = A0x(i1 +1, i2 +1)+A1x(i1 +1, i2)+A2x(i1, i2 +1). The algorithm is straightforward and has been implemented using the software package Matlab . Two step-by-step examples illustrating the application of the algorithm are presented.

The Laplacian, Second Order Elliptic Equations

On the Spectrum of a Class of Second Order Periodic Elliptic Differential Operators

Linear Elliptic Equations of Second Order

The classical Schauder type results on C-regularity of solutions are exposed for linear second order elliptic equations with Hölder coefficients. Our approach is based on equivalent seminorms in Hölder spaces C, which are similar to seminorms introduced by S. Campanato [1]. Under this approach, the C-estimates for solutions are derived from the maximum principle and the interior smoothness of h...