The Operator of a Boundary Value Problem With Chaplygin--Zhukovskii--Kutta Type Conditions on an Edge of the Boundary Has the Fredholm Property

S. A. Nazarov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 31 (1997) no. 3, pp. 44-56.

Bibliographie

[1] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987 | MR

[2] Sedov L. G., Ploskie zadachi gidromekhaniki i aerodinamiki, Nauka, M., 1980 | MR

[3] Belotserkovskii S. M., Nisht M. I., Nelineinye aerodinamicheskie kharakteristiki tonkogo kryla proizvolnoi formy v plane, Nauka, M., 1976

[4] Kutta M. W., “Auftriebskräfte in strömenden Flüssigkeiten”, Illustrierte Aëronautische Mitteilungen, 3 (1902), 133–138

[5] Zhukovskii N. E., “Geometricheskie issledovaniya o techenii Kutta”, Poln. sobr. soch., v. 5, ONTI, M.–L., 1937, 163–203

[6] Zhukovskii N. E., “O konturakh podderzhivayuschikh poverkhnostei aeroplanov”, Poln. sobr. soch., v. 5, ONTI, M.-L., 1937, 233–257

[7] Chaplygin S. A., “O davlenii ploskoparallelnogo potoka na pregrazhdayuschie tela (k teorii aeroplana)”, Matem. sb., 28:1 (1911), 120–166 | Zbl

[8] Reissner E., “Boundary value problems in aerodynamics of lifting surfaces in non-uniform motion”, Bull. Amer. Math. Soc., 55 (1949), 825–850 | DOI | MR | Zbl

[9] Meister E., Randwertaufgaben der Funktionentheorie, B. G. Teubner, Stuttgart, 1967 | MR

[10] Hinder R., Zur Problematik der KUTTA-Bedingung, Ph. D. thesis. THD, Darmstadt 78S, 1994

[11] Sternin B. Yu., “Ellipticheskie i parabolicheskie zadachi na mnogoobraziyakh s granitsei, sostoyaschei iz komponent razlichnoi razmernosti”, Trudy Mosk. matem. o-va, 15, 1966, 346–382 | MR | Zbl

[12] Nazarov S. A., Plamenevskii B. A., “Ellipticheskie zadachi s usloviyami izlucheniya na rebrakh granitsy”, Matem. sb., 183:10 (1992), 13–44 | MR

[13] Nazarov S. A., Plamenevskii B. A., “Samosopryazhennye zadachi s usloviyami izlucheniya na rebrakh granitsy”, Algebra i analiz, 4:3 (1992), 196–225 | Zbl

[14] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Trudy Mosk. matem. o-va, 16, 1967, 209–292

[15] Kondratev V. A., “Osobennosti reshenii zadachi Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka v okrestnosti rebra”, Differents. uravneniya, 13:11 (1977), 2026–2032 | MR

[16] Mazya V. G., Plamenevskii B. A., “Ob ellipticheskikh kraevykh zadachakh v oblastyakh s kusochno gladkoi granitsei”, Trudy simp. po mekh. sploshn. sred i rodstvennym probl. analiza, t. 1, Metsniereba, Tbilisi, 1973, 171–181

[17] Mazya V. G., Plamenevskii B. A., “Vesovye prostranstva s neodnorodnymi normami i kraevye zadachi v oblastyakh s konicheskimi tochkami”, Elliptishe Differentialgleichung (Meeting, Rostock, 1977), Wilhelm-Pieck-Univ., Rostock, 1978, 161–189 | MR

[18] Nikishkin V. A., “Osobennosti reshenii zadachi Dirikhle dlya uravneniya vtorogo poryadka v okrestnosti rebra”, Vestn. MGU, 1979, no. 2, 51–62 | MR | Zbl

[19] Maz'ya V. G., Rossmann J., “Uber die Asymptotik der Losungen elliptischer Randwertaufgaben in der Umgebung von Kanten”, Math. Nachr., 138 (1988), 27–53 | DOI | MR

[20] Grisvard P., Elliptic problems in non smooth domains, Pitman, London, 1985 | MR | Zbl

[21] Nazarov S. A., Plamenevskii B. A., Ellipticheskie zadachi v oblastyakh s kusochno gladkoi granitsei, Nauka, M., 1991; Nazarov S. A., Plamenevsky B. A., Elliptic problems in domains with piecewise smooth boundaries, Walter de Gruyter, Berlin, 1994 | MR

[22] Agmon S., Douglis A., Nirenberg L., “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, 1”, Comm. Pure Appl. Math., 12:4 (1959), 623–723 | DOI | MR

[23] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl