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

Published online by Cambridge University Press:  20 November 2018

David Kalaj
Affiliation:
Faculty of Mathematics, University of Montenegro, Dzordza Vašingtona bb, 81000 Podgorica, Montenegro. e-mail: davidkalaj@gmail.com e-mail: djordjijevuj@t-com.me
Djordjije Vujadinovic
Affiliation:
Faculty of Mathematics, University of Montenegro, Dzordza Vašingtona bb, 81000 Podgorica, Montenegro. e-mail: davidkalaj@gmail.com e-mail: djordjijevuj@t-com.me
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2017

References

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