Bernstein approximations of Dirichlet problems for elliptic operators on the plane
Date
2007-06-14
Authors
Gulgowski, Jacek
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We study the finitely dimensional approximations of the elliptic problem
(Lu)(x, y) + φ(λ, (x, y), u(x, y)) = 0 for (x, y) ∈ Ω
u(x, y) = 0 for (x, y) ∈ ∂Ω,
defined for a smooth bounded domain Ω on a plane. The approximations are derived from Bernstein polynomials on a triangle or on a rectangle containing Ω. We deal with approximations of global bifurcation branches of nontrivial solutions as well as certain existence facts.
Description
Keywords
Dirichlet problems, Bernstein polynomials, Global bifurcation
Citation
Gulgowski, J. (2007). Bernstein approximations of Dirichlet problems for elliptic operators on the plane. <i>Electronic Journal of Differential Equations, 2007</i>(86), pp. 1-14.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.