Geodesic
Bernstein approximations of Dirichlet problems for elliptic operators on the plane
Electronic journal of differential equations, Tome 2007 (2007)
We study the finitely dimensional approximations of the elliptic problem

$\displaylines{ (Lu)(x,y) + \varphi(\lambda,(x,y),u(x,y) ) = 0 \quad \hbox{for } (x,y)\in\Omega\cr u(x,y) = 0 \quad \hbox{for } (x,y)\in\partial\Omega, }$

defined for a smooth bounded domain $\Omega$ on a plane. The approximations are derived from Bernstein polynomials on a triangle or on a rectangle containing $\Omega$. We deal with approximations of global bifurcation branches of nontrivial solutions as well as certain existence facts.
Classification : 35J25, 41A10
Keywords: Dirichlet problems, Bernstein polynomials, global bifurcation 
@article{EJDE_2007__2007__a52,
     author = {Gulgowski,  Jacek},
     title = {Bernstein approximations of {Dirichlet} problems for elliptic operators on the plane},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1133.35039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a52/}
}
TY  - JOUR
AU  - Gulgowski,  Jacek
TI  - Bernstein approximations of Dirichlet problems for elliptic operators on the plane
JO  - Electronic journal of differential equations
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VL  - 2007
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%0 Journal Article
%A Gulgowski,  Jacek
%T Bernstein approximations of Dirichlet problems for elliptic operators on the plane
%J Electronic journal of differential equations
%D 2007
%V 2007
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%F EJDE_2007__2007__a52
Gulgowski,  Jacek. Bernstein approximations of Dirichlet problems for elliptic operators on the plane. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a52/