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Limits on the gradient of a harmonic function at the boundary of a domain

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Literature Cited

  1. S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  2. M. I. Vishik, “On an inequality for boundary values of harmonic functions in a sphere,” Usp. Mat. Nauk,6, No. 2, 165–166 (1951).

    Google Scholar 

  3. S. G. Mikhlin, “On an inequality for boundary values and harmonic functions,” Usp. Mat. Nauk,6, No. 6, 158–159 (1951).

    Google Scholar 

  4. N. M. Günter, Potential Theory and Its Application to the Fundamental Problems of Mathematical Physics [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  5. C. Miranda, Partial Differential Equations of Elliptic Type [Russian translation], IL, Moscow (1957).

    Google Scholar 

  6. L. N. Slobodetskii, “Generalized Sobolev spaces and their application to boundary value problems of partial differential equations,” Uch. Zap. Leningr. Ped. Inst. im Hertzen,197, 54–112 (1958).

    Google Scholar 

  7. S. M. Nikol'skii, Approximation of Functions of Many Variables and Embedding Theorems [in Russian], Fizmatgiz, Moscow (1969).

    Google Scholar 

  8. V. Blyashke, Circle and Sphere [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  9. G. Polya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  10. E. A. Volkov, “Derivation of a bound on the error in a numerical solution of the Dirichlet problem by known quantities,” in: Numerical Methods of Solution for Problems in Mathematical Physics [in Russian], Nauka, Moscow (1966), pp. 5–17.

    Google Scholar 

  11. I. D. Maergoiz, “Numerical solution of boundary value problems in potential theory by the method of integral equations, Sibirsk. Matem. Zh.,12, No. 6, 1318–1327 (1971).

    Google Scholar 

  12. L. V. Kantorovich and V. I. Krylov, Approximation Methods of Higher Analysis [in Russian], Gostekhizdat, Moscow-Leningrad (1952).

    Google Scholar 

  13. E. Goursat, Course of Mathematical Analysis [Russian translation], Vol. 3, Part 2, ONTI, Moscow-Leningrad (1934).

    Google Scholar 

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Authors
  1. I. D. Maergoiz
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 14, No. 6, pp. 1266–1284, November–December, 1973.

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Maergoiz, I.D. Limits on the gradient of a harmonic function at the boundary of a domain. Sib Math J 14, 890–903 (1973). https://doi.org/10.1007/BF00975895

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  • DOI: https://doi.org/10.1007/BF00975895

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