Estimates for Eigenfunctions of Elliptic Operators with Respect to the Spectral Parameter

V. Ya. Yakubov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 33 (1999) no. 2, pp. 58-67.

Bibliographie

[1] Smolitskii Kh. L., “Otsenki proizvodnykh fundamentalnykh funktsii”, DAN SSSR, 74:2 (1950), 205–208

[2] Eidus D. M., “Otsenki modulya sobstvennykh funktsii”, DAN SSSR, 90:6 (1953), 973–974 | MR

[3] Eidus D. M., “Nekotorye neravenstva dlya sobstvennykh funktsii”, DAN SSSR, 107:6 (1956), 796–798 | MR

[4] Ilin V. A., Shishmarev I. A., O tochnykh otsenkakh sobstvennykh funktsii v zamknutoi oblasti, Materialy k sovmestnomu sovetsko-amerikanskomu simpoziumu po uravneniyam v chastnykh proizvodnykh, Novosibirsk, 1963

[5] Ilin V. A., Shishmarev I. A., “Ravnomernye v zamknutoi oblasti otsenki dlya sobstvennykh funktsii ellipticheskogo operatora i ikh proizvodnykh”, Izv. AN SSSR, ser. matem., 24:6 (1960), 883–896 | MR

[6] Shishmarev I. A., Vvedenie v teoriyu ellipticheskikh uravnenii, Izd-vo MGU, 1979 | MR

[7] Shishmarev I. A., “Ravnomernye otsenki proizvodnykh reshenii zadachi Dirikhle i zadachi na sobstvennye funktsii dlya operatora $Lu=\operatorname{Div}(p(x)\operatorname{grad}u)+q(x)u$ s razryvnymi koeffitsientami”, DAN SSSR, 137:1 (1961), 45–47 | Zbl

[8] Ilin V. A., “O sisteme klassicheskikh sobstvennykh funktsii lineinogo samosopryazhennogo operatora s razryvnymi koeffitsientami”, DAN SSSR, 137:2 (1961), 272–275 | MR

[9] Ladyzhenskaya O. A., “Metod Fure dlya giperbolicheskikh uravnenii”, DAN SSSR, 74:3 (1950), 417–420 | Zbl

[10] Yakubov V. Ya., “Otsenki dlya normirovannykh v $L_2$ sobstvennykh funktsii ellipticheskogo operatora”, DAN SSSR, 274:1 (1984), 35–37 | MR | Zbl

[11] Yakubov V. Ya., Otsenki dlya sobstvennykh funktsii ellipticheskogo operatora s summiruemym koeffitsientom, Tezisy Vtoroi Severo-Kavkazskoi regionalnoi konferentsii. Funktsionalno-differentsialnye uravneniya i ikh prilozheniya, Makhachkala, 1989

[12] Yakubov V. Ya., “Tochnye otsenki dlya normirovannykh v $L_2$ sobstvennykh funktsii ellipticheskogo operatora”, Dokl. RAN, 331:3 (1993), 286–287 | MR | Zbl

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

[14] Nash J., “Continuity of solutions of parabolic and elliptic equations”, Amer. J. Math., 80:4 (1958), 931–954 ; Nesh Dzh., “O nepreryvnosti reshenii parabolicheskikh i ellipticheskikh uravnenii”, Matematika, 4:1 (1960), 31–52 | DOI | MR | Zbl

[15] De Giorgi E., “Sulla differenziabilita e l'analiticitâ delle estremali degli integrali multipli regolari”, Memorie delle Acc. Sci. Torino, Ser. 3, 1, 1957, 25–43, t. 3 ; De Dzhordzhi E., “O differentsiruemosti i analitichnosti ekstremalei kratnykh regulyarnykh integralov”, Matematika, 4:6 (1960), 23–38 | MR

[16] Stampacchia G., “Problemi al contorno elliptici con dati discontinui dotati di soluzioni Hölderiane”, Ann. Mat., 51 (1960), 1–38 | DOI | MR

[17] Kinderlerer D., Stampakkya G., Vvedenie v variatsionnye neravenstva i ikh prilozheniya, Mir, M., 1983 | MR

[18] Yakubov V. Ya., “Neklassicheskie dvustoronnie tochnye otsenki dlya normirovannykh sobstvennykh funktsii zadachi Shturma–Liuvillya”, Vestnik MGU, ser. 1, matem., mekhanika, 1993, no. 4, 37–44 | MR | Zbl

[19] Yakubov V. Ya., Spektralnye kraevye zadachi dlya differentsialnykh operatorov s negladkimi koeffitsientami, Doktorskaya dissertatsiya, MGU, 1996

[20] Gokhberg I. Ts., Krein M. G., Teoriya volterrovykh operatorov v gilbertovom prostranstve i ee prilozheniya, Nauka, M., 1967 | MR

[21] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR