Geodesic
Stability of Unique Solvability of Quasilinear Equations Given Additional Data
Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 918-946.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study quasilinear equations of elliptic and parabolic type whose solutions, having bounded uniform norms or bounded uniform norms of their derivatives, are uniquely defined by the additional information about the values of these solutions on a grid. For the case in which the equations and grid values are given with an error, we present estimates of the error of approximate solutions in the uniform metric.
Keywords: quasilinear equation of elliptic or parabolic type, stability of unique solvability, quasilinear equation, Dirichlet boundary-value problem, Banach space, Lipschitz function, $\varepsilon$-grid, star-shaped set, Friedrichs inequality. 
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I. G. Tsar'kov. Stability of Unique Solvability of Quasilinear Equations Given Additional Data. Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 918-946. http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a8/

[1] I. G. Tsarkov, “Ustoichivost odnoznachnoi razreshimosti v nekorrektnoi zadache Dirikhle”, Matem. zametki, 79:2 (2006), 294–308 | MR | Zbl

[2] I. G. Tsarkov, “Ustoichivost odnoznachnoi razreshimosti dlya nekotorykh differentsialnykh uravnenii”, Tr. IMM UrO RAN, 14, no. 3, 2008, 170–182

[3] S. I. Pokhozhaev, “Ob uravneniyakh vida $\Delta u=f(x,u,Du)$”, Matem. sb., 113:2 (1980), 324–338 | MR | Zbl

[4] E. Mitidieri, S. I. Pokhozhaev, “Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh”, Tr. MIAN, 234, Nauka, M., 2001, 3–383 | MR | Zbl

[5] I. G. Tsarkov, “O globalnom suschestvovanii neyavnoi funktsii”, Matem. sb., 184:7 (1993), 79–116 | MR | Zbl

[6] D. Gilbarg, N. Trudinger, Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[7] O. A. Ladyzhenskaya, N. N. Uraltseva, “Obzor rezultatov po razreshimosti kraevykh zadach dlya ravnomerno ellipticheskikh i parabolicheskikh kvazilineinykh uravnenii vtorogo poryadka, imeyuschikh neogranichennye osobennosti”, UMN, 41:5 (1986), 59–83 | MR | Zbl

[8] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR | Zbl

[9] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR | Zbl