The Venttsel' problem for nonlinear elliptic equations

Journal of Mathematical Sciences

Volumn 101, Issue 2, 2000, Pages 2861-2880

  Apushkinskaya, D E ^a   Nazarov, A I ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346952717     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/BF02672175     Document Type: Article

References (14)

1. D. E. Apushkinskaya and A. I. Nazarov, "A survey of results on nonlinear Venttsel' problems." Appl. Math., to appear.
2. D. E. Apushkinskaya and A. I. Nazarov, "On the quasilinear stationary Venttsel' problem," Zap. Nauchn. Semin. POMI, 221, 20-29 (1995).
3. D. E. Apushkinskaya and A. I. Nazarov, "Estimates for the gradient of solutions to stationary degenerate Venttsel' problems," J. Math. Sci., 98, No. 6, 654-673 (2000).
4. N. S. Trudinger, "Fully nonlinear, uniformly elliptic equations under natural structure conditions," Trans. Amer. Math. Soc., 278, 751-769 (1983).
5. G. M. Lieberman and N. S. Trudinger, "Nonlinear oblique boundary-value problems for nonlinear elliptic equations," Trans. Amer. Math. Soc., 295, 509-546 (1986).
6. D. E. Apushkinskaya and A. I. Nazarov, "Hölder estimates of solutions to initial-boundary value problems for parabolic equations of nondivergence form with Wentzel (Venttsel') boundary condition," Amer. Math. Soc. Transl., Ser. II, 164, 1-13 (1995).
7. O. A. Ladyzhenskaya and N. N. Ural'tseva. Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow (1973).
8. [English Translation of the 1st ed.: Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968)].
9. D. E. Apushkinskaya and A. I. Nazarov, "The initial-boundary value problem for nondivergence parabolic equations with Venttsel' boundary condition," St. Petersburg Math. J., 6, No. 6, 1127-1149 (1995).
10. G. M. Lieberman, "The Dirichlet problem for quasilinear elliptic equations with continuously difterentiable boundary data," Commun. Partial Differ. Equations, 11, No. 2, 167-229 (1986).
11. D. E. Apushkinskaya and A. I. Nazarov, "Boundary estimates for the first-order derivatives of a solution to a nondivergence parabolic equation with composite right-hand side and coefficients of lower-order derivatives," J. Math. Sci., 77, No. 4, 3257-3276 (1995).
12. O. V. Besov, V. P. Il'in. and S. M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Nauka, Moscow (1996).
13. [English Translation of the 1st ed.: Integral Representations of Functions and Embedding Theorems, Vol. I-II, Wiley, New York (1978, 1979).]
14. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin (1983).