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Vấn đề Venttsel cho các phương trình elliptic phi tuyến
Tóm tắt
Sự khả giải của vấn đề Venttsel' tĩnh hoàn toàn phi tuyến được thiết lập. Phương trình và điều kiện biên được giả định là elliptic đồng nhất. Tài liệu tham khảo: 12 tiêu đề.
Từ khóa
#Vấn đề Venttsel #phương trình elliptic phi tuyến #khả giảiTài liệu tham khảo
D. E. Apushkinskaya and A. I. Nazarov, “A survey of results on nonlinea Venttsel' problems”,Appl. Math., to appear.
D. E. Apushkinsakaya and A. I. Nazarov, “On the quasilinear stationary Venttsel' problem,”Zap. Nauchn. Semin. POMI,221, 20–29 (1995).
D. E. Apushkinsakaya and A. I. Nazarov, “Estimates for the gradient of solutions to stationary degenerate Venttsel' problems,”J. Math. Sci.,98, No. 6, 654–673 (2000).
N. S. Trudinger, “Fully nonlinear, uniformly elliptic equations under natural structure conditions,”Trans. Amer. Math. Soc.,278, 751–769 (1983).
G. M. Lieberman and N. S. Trudinger, “Nonlinear oblique bondary-value problems for nonlinear elliptic equations,”Trans. Amer. Math. Soc.,295, 509–546 (1986).
D. E. Apushkinsakaya 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).
O. A. Ladyzhenskaya and N. N. Ural'tseva,Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow (1973). [English Translation of the 1st ed,:Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968)].
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).
G. M. Lieberman, “The Dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data,”Commun. Partial Differ. Equations,11, No. 2, 167–229 (1986).
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).
O. V. Besov, V. P. Il'in, and S. M. Nikol'skii,Integral Represntations of Functions and Embedding Theorems [in Russian], Nauka, Moscow (1996). [English Translation of the 1st ed.:Integral Representations of Functions and Embedding Theorems, Vol. I–II, Wiley, New York (1978, 1979).]
D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin (1983).
