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Search: MSC category 35J05 ( Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] )

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1. CMB 2017 (vol 60 pp. 536)

Kalaj, David; Vujadinović, Djordjije
The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators
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
Categories:35J05, 47G10

2. CMB 2009 (vol 52 pp. 555)

Hirata, Kentaro
Boundary Behavior of Solutions of the Helmholtz Equation
This paper is concerned with the boundary behavior of solutions of the Helmholtz equation in $\mathbb{R}^\di$. In particular, we give a Littlewood-type theorem to show that the approach region introduced by Kor\'anyi and Taylor (1983) is best possible.

Keywords:boundary behavior, Helmholtz equation
Categories:31B25, 35J05

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