Geodesic
An Epi-Convergence Result for Bivariate Convex Functions
Journal of convex analysis, Tome 11 (2004) no. 1, pp. 197-208 
Adib Bagh. An Epi-Convergence Result for Bivariate Convex Functions. Journal of convex analysis, Tome 11 (2004) no. 1, pp. 197-208. http://geodesic.mathdoc.fr/item/JCA_2004_11_1_JCA_2004_11_1_a12/
@article{JCA_2004_11_1_JCA_2004_11_1_a12,
     author = {Adib Bagh},
     title = {An {Epi-Convergence} {Result} for {Bivariate} {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {197--208},
     year = {2004},
     volume = {11},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2004_11_1_JCA_2004_11_1_a12/}
}
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Voir la notice de l'article provenant de la source Heldermann Verlag

We prove that for a large class of convex and lower semi-continuous biavariate functions defined over RN, epi-convergence in one variable implies epi-convergence in both variables. We also show that for closed-valued and graph-convex mappings with domains with non empty interiors, pointwise convergence implies graph convergence. We provide a number of applications for both results.