A majorant of the Hölder constant is established for solutions of the two-phase quasilinear parabolic or elliptic boundary-value problems with degenerate and nondegenerate Venttsel conditions on an interface. In addition, gradient estimates for solutions of the two-phase quasilinear nondegenerate Venttsel problems are obtained, and the solvability in Sobolev and Hölder spaces is proved. Bibliography: 14 titles.
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Apushkinskaya, D.E., Nazarov, A.I. Quasilinear Two-Phase Venttsel Problems. Journal of Mathematical Sciences 115, 2704–2719 (2003). https://doi.org/10.1023/A:1023305432516
- Venttsel Problem