Abstract
We study some generalizations of the well-known problem of minimization of the Riesz energy on condensers. Under fairly general assumptions, we establish necessary and sufficient conditions for the existence of minimal measures.
Similar content being viewed by others
References
N. V. Zorii, “A noncompact variational problem in the theory of Riesz potentials,”Ukr. Mat. Zh.,47, No. 10, 1350–1360 (1995).
N. V. Zorii, “The problem of minimization of energy for space condensers and Riesz kernels,”Ukr. Mat. Zh.,41, No. 1, 34–41 (1989).
N. V. Zorii, “Variational problems in potential theory,”Ukr. Mat. Zh.,43, No. 3, 347–354 (1991).
N. S. Landkof,Foundations of Modern Potential Theory, Springer-Verlag, Berlin 1972.
O. Frostman, “Sur les fonctions surharmoniques d’ordre fractionnaire,”Ark. Mat.,26 A, No. 16 (1939).
B. Fuglede, “On the theory of potentials in locally compact spaces,”Acta Math.,103, No. 3–4, 139–215 (1960).
M. Ohtsuka, “On potentials in locally compact spaces,”J. Sci. Hiroshima Univ., Ser. A-l,25, No. 2, 135–352 (1961).
M. Brelot,Elements de la Theorie Classique du Potentiel, Paris (1961).
N. V. Zorii, “A noncompact minimum problem in the Riesz potential theory,” in:International Congress of Mathematicians. Abstracts of Brief Communications (Zurich, 1994), Zurich (1994), p. 114.
N. V. Zorii,The Problem of Minimization of Energy for Space Condensers [in Russian], Preprint No. 85.06, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1985).
N. V. Zorii, “The minimum Riesz energy problem for space condensers,” in:Abstracts of the International Conference on Potential Theory, Nagoya (1990).
Rights and permissions
About this article
Cite this article
Zorii, N.V. A noncompact variational problem in the theory of riesz potentials. II. Ukr Math J 48, 671–682 (1996). https://doi.org/10.1007/BF02384234
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02384234