Geodesic
From the Uniform Approximation of a Solution of the PDE to the L2-Approximation of the Gradient of the Solution
Journal of convex analysis, Tome 21 (2014) no. 1, pp. 237-252

Voir la notice de l'article provenant de la source Heldermann Verlag

We establish a new energy inequality for the difference of two semiconvex functions in a bounded open convex set D of Rn. This inequality is applied to the L2-approximation problem of the gradient of the unknown solution of the nonlinear elliptic partial differential equation provided that the latter solution is a semiconvex function in D.
Classification : 26B25, 35J60, 49L25
Mots-clés : Semiconvex and semiconcave functions, energy inequality, L-2-approximation, gradient of semiconvex function, convex envelope 
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     author = {K. Shashiashvili and M. Shashiashvili},
     title = {From the {Uniform} {Approximation} of a {Solution} of the {PDE} to the {L\protect\textsuperscript{2}-Approximation} of the {Gradient} of the {Solution}},
     journal = {Journal of convex analysis},
     pages = {237--252},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a12/}
}
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K. Shashiashvili; M. Shashiashvili. From the Uniform Approximation of a Solution of the PDE to the L2-Approximation of the Gradient of the Solution. Journal of convex analysis, Tome 21 (2014) no. 1, pp. 237-252. http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a12/