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Estimates for the gradient of solutions to stationary degenerate Venttsel' problems

Abstract

The stationary Venttsel' problem for a uniformly elliptic operator is studied. Elliptic terms of the boundary operator can degenerate, whereas the first-order terms form a nondegenerate nontangent operator. The maximum and the Hölder norm for the tangent gradient of a solution to the problem are estimated. An estimate for the Hölder norm of the full gradient is also derived. Bibliography: 11 titles.

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Additional information

To the memory of Evgenii Mikhailovich Landis

Translated fromProblemy Matematicheskogo Analiza, No. 18, 1998, pp. 43–69.

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Apushkinskaya, D.E., Nazarov, A.I. Estimates for the gradient of solutions to stationary degenerate Venttsel' problems. J Math Sci 98, 654–673 (2000). https://doi.org/10.1007/BF02355382

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Keywords

  • Boundary Operator
  • Elliptic Operator
  • Stationary Degenerate
  • Full Gradient
  • Tangent Gradient