Geodesic
The conditions of a local minimum of a function in two variable at boundary points
Trudy Instituta matematiki, Tome 17 (2009) no. 2, pp. 35-44

Voir la notice de l'article provenant de la source Math-Net.Ru

The relation between a local minimum conditions of a real analytic function in two variables at boundary points and the method of Newton diagram are described. 
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     title = {The conditions of a local minimum of a function in two variable at boundary points},
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A. V. Krivko-Krasko. The conditions of a local minimum of a function in two variable at boundary points. Trudy Instituta matematiki, Tome 17 (2009) no. 2, pp. 35-44. http://geodesic.mathdoc.fr/item/TIMB_2009_17_2_a3/