The solution operator of the inhomogeneous Dirichlet problem in the unit ball

Kalaj, David; Vujadinovic, Djordjije

doi:10.1090/proc/12723

Cited by 6 publications

(4 citation statements)

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“…where V is the n-dimensional Lebesgue volume measure and G(η, ξ), η = ξ, is the usual Green function [18,22,23], i.e. G(η, ξ) =    1 2π log 1−ηξ η−ξ , for n = 2, 1 (n−2)ω n−1 |η − ξ| 2−n − ξ|η| − ξ/|ξ| 2−n , for n ≥ 3.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…It is well known that if u satisfies the conditions: (1) ∆u = ψ which is continuous in B n with n ≥ 2, and (2) u | S n−1 = φ which is bounded and integrable in S n−1 , then (cf. [15, p. 118-119] or [18,22,23])…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…where V is the n-dimensional Lebesgue volume measure and G(η, ξ), η = ξ, is the usual Green function [18,22,23], i.e.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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On Lipschitz continuity of solutions of hyperbolic Poisson’s equation

et al. 2017

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In this paper, we investigate solutions of the hyperbolic Poisson equa-is the hyperbolic Laplace operator in the n-dimensional space R n for n ≥ 2. We show that if n ≥ 3 andHere P h and G h denote Poisson and Green integrals with respect to ∆ h , respectively. Furthermore, we prove that functions of the form uwhere η ∈ B n and σ is the (n − 1)-dimensional Lebesgue measure normalized so that σ(S n−1 ) = 1. Moreover, Kalaj [16] also proved the Lipschitz continuity of 2000 Mathematics Subject Classification. Primary: 31B05; Secondary: 31C05.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Section: Introduction and Main Resultsmentioning

confidence: 99%