On the Hölder continuity of solutions of the Venttsel’ elliptic problem

Abstract

For solutions of the Venttsel’ problem in divergence form, a local Hölder estimate is obtained. It is shown that Harnack’s inequality in classical form does not hold.

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Correspondence to A. I. Nazarov.

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Original Russian Text © A.I. Nazarov, A.A. Paletskikh, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 5, pp. 532–536.

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Nazarov, A.I., Paletskikh, A.A. On the Hölder continuity of solutions of the Venttsel’ elliptic problem. Dokl. Math. 92, 747–751 (2015). https://doi.org/10.1134/S1064562415060307

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Keywords

  • Steklov Institute
  • DOKLADY Mathematic
  • Integral Identity
  • Lower Order Term
  • Cauchy Inequality