Geodesic
Bernstein approximations of Dirichlet problems for elliptic operators on the plane
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a152,
     author = {Gulgowski, Jacek},
     title = {Bernstein approximations of {Dirichlet} problems for elliptic operators on the plane},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a152/}
}
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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__a152/