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Hölder estimates for solutions to the degenerate boundary-value Venttsel' problem for parabolic and elliptic equations of nondivergence type

Abstract

The authors continue to study the Venttsel' problem, i.e., the boundary-value problem for a parabolic or elliptic equation with the boundary condition in the form of a parabolic or elliptic equation with respect to tangent variables. A priori estimates for the Hölder norms of solutions are established in the case of quasilinear equations of nondivergence form with a quasilinear degenerate boundary Venttsel' condition. Bibliography: 16 titles.

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Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 3–19.

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Apushkinskaya, D.E., Nazarov, A.I. Hölder estimates for solutions to the degenerate boundary-value Venttsel' problem for parabolic and elliptic equations of nondivergence type. J Math Sci 97, 4177–4188 (1999). https://doi.org/10.1007/BF02365038

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Keywords

  • Boundary Condition
  • Elliptic Equation
  • Quasilinear Equation
  • Tangent Variable
  • Nondivergence Form