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
Contact details are reproduced from the original publication and may be historical.
Kakha Shashiashvili
I. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences, 2 University Street, Tbilisi 0186, Georgia
Malkhaz Shashiashvili
A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2 University Street, Tbilisi 0186, Georgia
mshashiashvili@yahoo.comSuggested citation
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. https://doi.org/10.68381/jca21013
Published by Heldermann Verlag, 2014. Rights now held by Banach Press.
Kakha Shashiashvili
