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Equilibrium Potentials with External Fields

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Ukrainian Mathematical Journal Aims and scope

Abstract

We investigate the Gauss variational problem over fairly general classes of Radon measures in a locally compact space X. We describe potentials of minimizing measures, establish their characteristic properties, and prove the continuity of extremals. Extremal problems dual to the original one are formulated and solved. The results obtained are new even in the case of classical kernels and the Euclidean space \(\mathbb{R}^n \).

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REFERENCES

  1. M. Ohtsuka, “On potentials in locally compact spaces,” J. Sci. Hiroshima Univ. Ser. A-1, 25, No. 2, 135-352 (1961).

    Google Scholar 

  2. N. V. Zorii, On Equilibrium Problems for Potentials with External Fields, Preprint No. 2002.07, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002).

    Google Scholar 

  3. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer, Berlin (1997).

    Google Scholar 

  4. N. S. Landkof, Foundations of Modern Potential Theory [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  5. N. Bourbaki, Integration. Measures. Integration of Measures [Russian translation], Nauka, Moscow (1967).

    Google Scholar 

  6. R. E. Edwards, Functional Analysis. Theory and Applications, Holt, Rinehart & Winston, New York (1965).

    Google Scholar 

  7. B. Fuglede, “On the theory of potentials in locally compact spaces,” Acta Math., 103, No. 3-4, 139-215 (1960).

    Google Scholar 

  8. N. V. Zorii, “Extremal problems in the theory of capacities of condensers in locally compact spaces. I,” Ukr. Mat. Zh., 53, No. 2, 168-189 (2001).

    Google Scholar 

  9. N. V. Zorii, “Extremal problems in the theory of capacities of condensers in locally compact spaces. II,” Ukr. Mat. Zh., 53, No. 4, 466-488 (2001).

    Google Scholar 

  10. N. V. Zorii, “Extremal problems in the theory of capacities of condensers in locally compact spaces. III,” Ukr. Mat. Zh., 53, No. 6, 758-782 (2001).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    N. V. Zorii

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  1. N. V. Zorii
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Zorii, N.V. Equilibrium Potentials with External Fields. Ukrainian Mathematical Journal 55, 1423–1444 (2003). https://doi.org/10.1023/B:UKMA.0000018005.67743.86

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  • DOI: https://doi.org/10.1023/B:UKMA.0000018005.67743.86

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