Theorems of Phragmén–Lindelöf type for linear elliptic equations of second order
Sbornik. Mathematics, Tome 11 (1970) no. 4, pp. 467-490 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a linear uniformly elliptic equation of second order. Under various assumptions regarding the coefficients we study the character of the growth of a solution defined in an unbounded domain and vanishing on the boundary of the domain. Estimates are obtained in terms of capacity. Bibliography: 21 titles.
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     author = {G. N. Blokhina},
     title = {Theorems of {Phragm\'en{\textendash}Lindel\"of} type for linear elliptic equations of second order},
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     year = {1970},
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G. N. Blokhina. Theorems of Phragmén–Lindelöf type for linear elliptic equations of second order. Sbornik. Mathematics, Tome 11 (1970) no. 4, pp. 467-490. http://geodesic.mathdoc.fr/item/SM_1970_11_4_a0/

[1] M. V. Keldysh, “O razreshimosti i ustoichivosti zadachi Dirikhle”, Uspekhi matem. nauk, 1941, no. 8, 171–231 | MR | Zbl

[2] E. M. Landis, “Nekotorye voprosy kachestvennoi teorii ellipticheskikh i parabolicheskikh uravnenii”, Uspekhi matem. nauk, XIV:1(85) (1959), 21–85 | MR

[3] E. M. Landis, “Nekotorye voprosy kachestvennoi teorii ellipticheskikh uravnenii vtorogo poryadka (sluchai mnogikh nezavisimykh peremennykh)”, Uspekhi matem. nauk, XVIII:1(109) (1963), 3–62 | MR

[4] E. M. Landis, Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, ch. I, MGU, Moskva, 1967

[5] E. M. Landis, Uravneniya s chastnymi proizvodnymi, ch. 2, MGU, Moskva, 1968

[6] R. Nevanlinna, Odnoznachnye analiticheskie funktsii, Gostekhizdat, Moskva–Leningrad, 1941 | MR

[7] M. A. Evgrafov, “Obobschenie teorem Fragmena–Lindelëfa dlya analiticheskikh funktsii na resheniya drugikh ellipticheskikh sistem”, Izv. AN SSSR, seriya matem., 27 (1963), 843–854 | MR | Zbl

[8] D. Gilbarg, D. Serrin, “Izolirovannye osobennosti reshenii ellipticheskikh differentsialnykh uravnenii vtorogo poryadka”, Matematika, 2:6 (1958), 63–86

[9] D. Serrin, “O neravenstve Garnaka dlya lineinykh ellipticheskikh uravnenii”, Matematika, 2:6 (1958), 49–62

[10] K. Miranda, Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, IL, Moskva, 1957

[11] V. A. Kondratev, “O razreshimosti kraevoi zadachi dlya ellipticheskikh uravnenii”, DAN SSSR, 136:4 (1961), 771–774

[12] G. N. Blokhina, “Teoremy tipa Fragmena–Lindelëfa dlya lineinogo ellipticheskogo uravneniya vtorogo poryadka”, DAN SSSR, 162:4 (1965), 727–730 | Zbl

[13] R. M. Herve, “Recherches axiomatiques sur la theorie des fonctions surharmomiques et du potentiel”, Ann. Inst. Fourier, 12 (1962), 415–571 | MR | Zbl

[14] I. O. Herzog, “Phragmen–Lindelöf theorems for second order quasi-linear elliptic partial differential equations”, Proc. Amer. Math. Soc., 15:5 (1964), 721–728 | DOI | MR | Zbl

[15] A. Dinghas, “Über einige Konvexitätstragen bei partiellen Differential-gleichungen vom Sturmschen Typus”, Math. Ann., 115 (1964), 397–421 | DOI | MR

[16] P. C. Fife, “Growth and decay properties of solutions of second order elliptic equations”, Ann. Scuola Norm. Super. Pisa, 20:4 (1966), 675–701 | MR | Zbl

[17] V. G. Mazya, “O regulyarnosti na granitse reshenii ellipticheskikh uravnenii i konformnogo otobrazheniya”, DAN SSSR, 152:6 (1963), 1297–1300

[18] V. G. Mazya, Problemy matematicheskogo analiza. Kraevye zadachi i integralnye uravneniya, LGU, Leningrad, 1966 | MR

[19] G. M. Verzhbinskii, V. G. Mazya, “Ob asimptotike reshenii zadachi Dirikhle vblizi neregulyarnoi granitsy”, DAN SSSR, 176:3 (1967), 498–501 | Zbl

[20] V. G. Mazya, “O povedenii vblizi granitsy resheniya zadachi Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka v divergentnoi forme”, Matem. zametki, 2:2 (1967), 209–220

[21] U. Littman, G. Stampakkya, G. F. Veinberger, “Regulyarnye tochki dlya ellipticheskikh uravnenii s razryvnymi koeffitsientami”, Matematika, 9:2 (1965), 72–97