The study of the equation (L₂L₁)*h = 0 or of the equivalent system L*₂h₂ = -h₁, L*₁h₁ = 0, where is a second order elliptic differential operator, leads us to the following general framework: Starting from a biharmonic space, for example the space of solutions (u₁,u₂) of the system L₁u₁ = -u₂, L₂u₂ = 0, being elliptic or parabolic, and by means of its Green pairs, we construct the associated adjoint biharmonic space which is in duality with the initial one.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-1-1,
author = {Emmanuel P. Smyrnelis},
title = {Fonctions biharmoniques adjointes},
journal = {Annales Polonici Mathematici},
volume = {98},
year = {2010},
pages = {1-21},
zbl = {1206.31006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-1-1}
}
Emmanuel P. Smyrnelis. Fonctions biharmoniques adjointes. Annales Polonici Mathematici, Tome 98 (2010) pp. 1-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-1-1/