Abstract
A monotonicity property and a refined estimate of Harnack inequality are derived for positive solutions of the Weinstein equation.
A monotonicity property and a refined estimate of Harnack inequality are derived for positive solutions of the Weinstein equation.
Ö. Akın and H. Leutwiler, “On the invariance of the solutions of the Weinstein equation under Möbius transformations,” in Classical and Modern Potential Theory and Applications, K. GowriSankaran, J. Bliedtner, D. Feyel, M. Goldstein, W. K. Hayman, and I. Netuka, Eds., vol. 430 of NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences, pp. 19–29, Kluwer Academic, Dordrecht, The Netherlands, 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC. Liu and L. Peng, “Boundary regularity in the Dirichlet problem for the invariant Laplacians on the unit real ball,” Proceedings of the American Mathematical Society, vol. 132, no. 11, pp. 3259–3268, 2004.
View at: Publisher Site | Google Scholar | MathSciNetM. Kassmann, “Harnack inequalities: an introduction,” Boundary Value Problems, vol. 2007, Article ID 81415, 21 pages, 2007.
View at: Publisher Site | Google Scholar | MathSciNetH. Leutwiler, “Best constants in the harnack inequality for the Weinstein equation,” Aequationes Mathematicae, vol. 34, no. 2-3, pp. 304–315, 1987.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. Huber, “On the uniqueness of generalized axially symmetric potentials,” Annals of Mathematics, vol. 60, no. 2, pp. 351–358, 1954.
View at: Publisher Site | Google ScholarB. Brelot-Collin and M. Brelot, “Représentation intégrale des solutions positives de l'équation , ( constante réelle) dans le demi-espace , de ,” Bulletin de la Classe des Sciences. Académie Royale de Belgique, vol. 58, pp. 317–326, 1972.
View at: Google Scholar | Zentralblatt MATH | MathSciNet