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

Journal of Mathematical Sciences

Volumn 98, Issue 6, 2000, Pages 654-673

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

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52849111906     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/BF02355382     Document Type: Article

References (12)

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2. D. E. Apushkinskaya and A. I. Nazarov, "On the quasilinear stationary Venttsel' problem," Zap. Nauchn. Semin. POMI, 221, 20-29 (1995).
3. K. S. Tulenbaev and N. N. Ural'tseva, "A nonlinear boundary value problem for elliptic equations of general form," Partial Differential Equations, Inst. Mat. Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk (1987), pp. 95-112.
4. G. M. Lieberman and N. S. Trudinger, "Nonlinear oblique boundary value problems for nonlinear elliptic equations," Trans. Amer. Math. Soc., 295, 509-546 (1986).
5. D. E. Apushkinskaya and A. I. Nazarov, Hölder Estimates of Solutions to Degenerate Venttsel' Boundary Value Problems for Parabolic and Elliptic Equations of Nondivergent Form, Research report, Austral. Nat. Univ., Centre Math. Analysis, MRR 006-97 (1997).
6. N. S. Trudinger, "Fully nonlinear, uniformly elliptic equations under natural structure conditions," Trans. Amer. Math. Soc., 278, 751-769 (1983).
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, "Holder estimates of solutions to initial-boundary value problems for parabolic equations of nondivergent form with Wentzel (Venttsel') boundary condition," Amer. Math. Soc. Transl., Ser. II, 164, 1-13 (1995).
10. O. A. Ladyzhenskaya and N. N. Ural'tseva, "Estimates of the Holder constant for functions satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality with unbounded coefficients," Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova, 147, 72-94 (1985).
11. D. E. Apushkinskaya and A. I. Nazarov, Gradient Estimates for Solutions of Stationary Degenerate Venttsel' Problems. I, Research report MRR 058-97, Austral. Nat. Univ., Centre Math. Analysis (1997).
12. D. E. Apushkinskaya and A. I. Nazarov, Gradient Estimates for Solutions of Stationary Degenerate Venttsel' Problems. II, Research report MRR 019-98, Austral. Nat. Univ., Centre Math. Analysis (1998).