On Phragme'n - Lindelo"f principle for non-divergence type elliptic equations and mixed boundary conditions
Автор: Ibraguimov Akif, Nazarov Alexander I.
Журнал: Математическая физика и компьютерное моделирование @mpcm-jvolsu
Рубрика: Математика
Статья в выпуске: 3 (40), 2017 года.
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The paper is dedicated to qualitative study of the solution of the Zaremba-type problem in Lipschitz domain with respect to the elliptic equation in non-divergent form. Main result is Landis type Growth Lemma in spherical layer for Mixed Boundary Value Problem in the class of “admissible domain”. Based on the Growth Lemma Phragme´n - Lindelo¨ f theorem is proved at junction point of Dirichlet boundary and boundary over which derivative in non-tangential direction is defined.
Elliptic equation in non-divergent form, mixed boundary value problem, growth lemma, phragme´n - lindelo¨ f theorem, zaremba-type problem
Короткий адрес: https://sciup.org/14968910
IDR: 14968910 | DOI: 10.15688/mpcm.jvolsu.2017.3.5
Список литературы On Phragme'n - Lindelo"f principle for non-divergence type elliptic equations and mixed boundary conditions
- Aimar H., Forzani L., Toledano R. Ho¨ lder regularity of solutions of PDE’s: a geometrical view. Comm. PDE, 2001, vol. 26, no. 7-8, pp. 1145-1173.
- Alkhutov Yu.A. On the regularity of boundary points with respect to the Dirichlet problem for second-order elliptic equations. Math. Notes, 1981, vol. 30, no. 3, pp. 655-660.
- Kerimov T.M., Maz’ya V.G., Novruzov A.A. An analogue of the Wiener criterion for the Zaremba problem in a cylindrical domain. Funct. Analysis and Its Applic., 1982, vol. 16, no. 4, pp. 301-303.
- Landis E.M. On some properties of the solutions of elliptic equations. Dokl. Akad. Nauk SSSR, 1956, vol. 107, no. 4, pp. 640-643.
- Landis E.M. s-capacity and its application to the study of solutions of a second order elliptic equation with discontinuous coefficients. Math. USSR-Sb., 1968, vol. 5, no. 2, pp. 177-204.
- Landis E.M. Second Order Equations of Elliptic and Parabolic Type. Providence, Rhode Island, AMS, 1998. 278 p.
- Landis E.M. Some problems of the qualitative theory of elliptic and parabolic equations. UMN, 1959, vol. 14, no. 1 (85), pp. 21-85.
- Landis E.M. Some problems of the qualitative theory of second order elliptic equations (case of several independent variables). Russian Math. Surveys, 1963, vol. 18, no. 1, pp. 1-62.
- Maz’ya V.G. The behavior near the boundary of the solution of the Dirichlet problem for an elliptic equation of the second order in divergence form. Math. Notes, 1967, vol. 2, no. 2, pp. 610-617.
- Nadirashvili N.S. Lemma on the interior derivative and uniqueness of the solution of the second boundary value problem for second-order elliptic equations. Dokl. Akad. Nauk SSSR, 1981, vol. 261, no. 4, pp. 804-808.
- Nadirashvili N.S. On the question of the uniqueness of the solution of the second boundary value problem for second-order elliptic equations. Math. USSR-Sb., 1985, vol. 50, no. 2, pp. 325-341.
- Safonov M.V. Non-divergence Elliptic Equations of Second Order with Unbounded Drift. Amer. Math. Soc. Transl. Ser. 2. Providence, RI, AMS, 2010, vol. 229, pp. 211-232.
