Geodesic
On the behavior at infinity of solutions of second order elliptic equations in domains with noncompact boundary
Sbornik. Mathematics, Tome 40 (1981) no. 4, pp. 527-548 
O. A. Oleinik; G. A. Iosif'yan. On the behavior at infinity of solutions of second order elliptic equations in domains with noncompact boundary. Sbornik. Mathematics, Tome 40 (1981) no. 4, pp. 527-548. http://geodesic.mathdoc.fr/item/SM_1981_40_4_a3/
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     title = {On the behavior at infinity of solutions of second order elliptic equations in domains with noncompact boundary},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the behavior at infinity of solutions of second order elliptic equations is studied. Here the solutions satisfy homogeneous Dirichlet conditions, Neumann conditions or periodicity conditions, in each case on the part of the boundary that belongs to some neighborhood of infinity. The authors obtain a priori estimates characterizing the behavior, as $|x|\to\infty$, of these solutions in domains with noncompact boundary, depending on the geometric properties of the domain and the behavior, again as $|x|\to\infty$, of the function $f(x)$ on the right side of the equation. Bibliography: 13 titles.

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[2] O. A. Oleinik, G. A. Yosifian, “On singularities at the boundary points and uniqueness theorems for solutions of the first boundary problem of elasticity”, Comm. Part. Eq., 2:9 (1977), 937–969 | DOI | MR | Zbl

[3] E. M. Landis, G. P. Panasenko, “Ob odnom variante teoremy tipa Fragmena–Lindelefa dlya ellipticheskikh uravnenii s koeffitsientami, periodicheskimi po vsem peremennym, krome odnoi”, Trudy seminara im. I. G. Petrovskogo, vyp. 5, izd-vo MGU, 1979, 105–136 | MR

[4] G. P. Panasenko, “Asimptotiki vysshikh poryadkov reshenii uravnenii s bystro ostsilliruyuschimi koeffitsientami”, DAN SSSR, 240:6 (1978), 1293–1296 | MR | Zbl

[5] E. De Giorgi, “Sulla differenziabilita e l'analiticita delle estremali degli integrali multipli regolari”, Mem. Ace. Sci. Torino, 3 (1957), 1–19

[6] G. Stampacchia, “Le probleme de Dirichlet pour les equations elliptique du second ordre a coefficientes discontinue”, Ann. Inst. Fourier, Grenoble, 15 (1965), 189–258 | MR | Zbl

[7] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, izd-vo “Nauka”, Moskva, 1973 | MR

[8] C. Miranda, Partial differential equations of elliptic type, Springer-Verlag, 1970 | MR

[9] P. Kurant, D. Gilbert, Metody matematicheskoi fiziki, t. I, Gostekhizdat, Moskva–Leningrad, 1951

[10] L. E. Payne, “Isoperimetric inequalities and their applications”, SIAM Review., 9:3 (1967), 453–488 | DOI | MR | Zbl

[11] J. H. Bramble, L. E. Payne, “Bounds in the Neuman problem for second order unformly elliptic operators”, Pacific J. Math., 12 (1962), 823–833 | MR | Zbl

[12] L. Bers, F. Dzhon, M. Shekhter, Uravneniya s chastnymi proizvodnymi, izd-vo “Mir”, Moskva, 1966 | MR

[13] S. N. Kruzhkov, “Kraevye zadachi dlya vyrozhdayuschikhsya ellipticheskikh uravnenie vtorogo poryadka”, Matem. sb., 77(119) (1968), 299–334 | Zbl