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Abstract
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.
Author information
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KS
Kakha Shashiashvili
I. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences, 2 University Street, Tbilisi 0186, Georgia
MS
Malkhaz Shashiashvili
A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2 University Street, Tbilisi 0186, Georgia
K. Shashiashvili, M. Shashiashvili. “From the Uniform Approximation of a Solution of the PDE to the L^(2)-Approximation of the Gradient of the Solution.” Journal of Convex Analysis 21 (2014), No. 1, 237–252.