Geodesic
Generalized solutions of the linear boundary value problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2019), pp. 25-36.

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

We use constructions from the general theory of boundary value problems to build a theory of generalized boundary value problems for the generalized Poisson equation. Namely, generalized solutions of various boundary value problems are introduced and studied for the matrix generalization of the Poisson equation, a description of the set of all such well-posed problems is given. The results obtained are used for advancements in the original general theory of boundary value problems.
Keywords: general theory of boundary value problems, extensions of differential operators, generalized statements, generalized solutions. 
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V. P. Burskii. Generalized solutions of the linear boundary value problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2019), pp. 25-36. http://geodesic.mathdoc.fr/item/IVM_2019_12_a2/

[1] Vishik M. I., “Ob obschikh kraevykh zadachakh dlya ellipticheskikh differentsialnykh uravnenii”, Tr. Mosk. Matem. o-va, 1, 1952, 187–246 | Zbl

[2] Khermander L., K teorii obschikh differentsialnykh operatorov v chastnykh proizvodnykh, IL, M., 1959

[3] Berezanskii Yu. M., Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Nauk. dumka, Kiev, 1965

[4] Agranovich M. S., “Ob uravneniyakh v chastnykh proizvodnykh s postoyannymi koeffitsientami”, Uspekhi matem. nauk, 16:2 (1961), 27–93 | MR | Zbl

[5] Dezin A. A., Obschie voprosy teorii granichnykh zadach, Nauka, M., 1980

[6] Petrovskii I. G., “O nekotorykh problemakh teorii uravnenii s chastnymi proizvodnymi”, Uspekhi matem. nauk, 1:3–4 (1946), 44–70 | Zbl

[7] Lopatinskii Ya. B., “Ob odnom sposobe svedeniya kraevykh zadach dlya sistem differentsialnykh uravnenii ellipticheskogo tipa k regulyarnym integralnym uravneniyam”, Ukr. matem. zhurn., 5:2 (1953), 123–151

[8] Bitsadze A. V., Nekotorye klassy differentsialnykh uravnenii s chastnymi proizvodnymi, Nauka, M., 1981

[9] Soldatov A. P., “Singulyarnye integralnye operatory i ellipticheskie kraevye zadachi. I”, Funktsionalnyi an., SMFN, 63, no. 1, 2017, 1–189

[10] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, FM, M., 1973

[11] Burskii V. P., “O granichnykh svoistvakh reshenii differentsialnykh uravnenii i obschikh granichnykh zadachakh”, Tr. Moskovsk. Matem. o-va, 68, 2007, 185–225

[12] Burskii V. P., “Obobschennye resheniya granichnykh zadach dlya differentsialnykh operatorov obschego vida”, UMN, 53:4 (1998), 215–216 | DOI

[13] Burskii V., “On well-posedness of boundary value problems for some class of general PDEs in a generalized setting”, Functional Diff. Equ., 8:1–2 (2001), 89–100 | MR | Zbl

[14] Maklein S., Gomologiya, Mir, M., 1966

[15] Uitni Kh., Geometricheskaya teoriya integrirovaniya, IL, M., 1960