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The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators

Published:2017-05-23
Printed: Sep 2017
• David Kalaj,
Faculty of Mathematics, University of Montenegro, Dzordza Vašingtona bb, 81000 Podgorica, Montenegro
In this paper we determine the $L^1\to L^1$ and $L^{\infty}\to L^\infty$ norms of an integral operator $\mathcal{N}$ related to the gradient of the solution of Poisson equation in the unit ball with vanishing boundary data in sense of distributions.