Ausstrahlungsproblem des Laplace-Operators für eine Klasse der Gebiete mit unbeschränktem Rand.
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u(x 1, x 2) at the vertices of a regular triangulation T h composed both of rectangles and triangles is presented. The method assumes that only the interpolant Πh[u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from T h is known. A complete analysis of this method is an extension of the complete analysis concerning the finite...
By using averaging techniques, some oscillation criteria for quasilinear elliptic differential equations of second order are obtained. These results extend and generalize the criteria for linear differential equations due to Kamenev, Philos and Wong.
We investigate the behaviour of a sequence , s = 1,2,..., of eigenvalues of the Dirichlet problem for the p-Laplacian in the domains , s = 1,2,..., obtained by removing from a given domain Ω a set whose diameter vanishes when s → ∞. We estimate the deviation of from the eigenvalue of the limit problem. For the derivation of our results we construct an appropriate asymptotic expansion for the sequence of solutions of the original eigenvalue problem.