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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
  • Djordjije Vujadinović,
    Faculty of Mathematics, University of Montenegro, Dzordza Vašingtona bb, 81000 Podgorica, Montenegro
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Abstract

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.
Keywords: Möbius transformation, Poisson equation, Newtonian potential, Cauchy transform, Bessel function Möbius transformation, Poisson equation, Newtonian potential, Cauchy transform, Bessel function
MSC Classifications: 35J05, 47G10 show english descriptions Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]
Integral operators [See also 45P05]
35J05 - Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]
47G10 - Integral operators [See also 45P05]
 

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