Geodesic
Unimprovable estimates in Hölder spaces for generalized solutions of the Dirichlet problem for a class of fourth order elliptic equations
Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 429-446 Cet article a éte moissonné depuis la source Math-Net.Ru

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Generalized solutions of the Dirichlet problem for a fourth order elliptic equation in two independent variables are investigated. Unimprovable estimates are obtained for the modulus of the generalized solution and its first derivatives in the neighborhood of a boundary point; it is also proved that the generalized solutions belong to a Hölder space with an unimprovable index depending on the geometry of the domain. Bibliography: 16 titles. 
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     author = {D. M. Lekveishvili},
     title = {Unimprovable estimates in {H\"older} spaces for generalized solutions of the {Dirichlet} problem for a~class of fourth order elliptic equations},
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     pages = {429--446},
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D. M. Lekveishvili. Unimprovable estimates in Hölder spaces for generalized solutions of the Dirichlet problem for a class of fourth order elliptic equations. Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 429-446. http://geodesic.mathdoc.fr/item/SM_1987_56_2_a9/

[1] Muskhelishvili N. I., Nekotorye osnovnye zadachi teorii uprugosti, Nauka, M., 1966

[2] Lomakin V. A., “Ploskaya zadacha teorii uprugosti mikroneodnorodnykh tel”, Izv. AN SSSR. Ser. mekh. tv. tela, 1966, no. 3, 72–77 | Zbl

[3] Duvaut G., “Comportement macroscopique d'une plaque perforee periodiquement”, Lect. Motes in Math., 594, 1976, 131–145 | DOI | MR

[4] Oleinik O. A., Iosifyan G. A., “Printsip Sen-Venana v ploskoi teorii uprugosti i kraevye zadachi dlya bigarmonicheskogo uravneniya v neogranichennykh oblastyakh”, Sib. mat. zhurn., 19:5 (1978), 1154–1165 | MR | Zbl

[5] Oleinik O. A., Iosifyan G. A., Tavkhelidze I. N., “Otsenki reshenii bigarmonicheskogo uravneniya v okrestnosti neregulyarnykh tochek granitsy i na beskonechnosti”, UMN, 33:3 (1978), 181–182 | MR | Zbl

[6] Oleinik O. A., Iosifyan G. A., Tavkhelidze I. N., “O povedenii reshenii uravnenii ploskoi teorii uprugosti v okrestnosti neregulyarnykh tochek granitsy i na beskonechnosti”, Differentsialnye i integralnye uravneniya. Kraevye zadachi, Tbilisi, 1979, 237–255 | MR | Zbl

[7] Kondratev V. A., Kopachek I., Oleinik O. A., “Otsenki modulya resheniya bigarmonicheskogo uravneniya i ego pervykh proizvodnykh v okrestnosti neregulyarnoi granichnoi tochki”, UMN, 36:4 (1981), 230–231

[8] Kondratev V. A., Kopachek I., Oleinik O. A., “Ob asimptoticheskikh svoistvakh reshenii bigarmonicheskogo uravneniya”, Differents. uravneniya, 17:10 (1981), 1886–1899 | MR | Zbl

[9] Kondratiev V. A., Olelnik O. A., “Estimates for solutions of the Dirichlet problem for biharmonic equation in a neighbourhood of an irregular boundary point and an neibourhood of infinity. Saint-Venant's principle”, Proc. Roy. Soc. Edinburgh A, 93 (1983), 327–343 | MR | Zbl

[10] Kondratev V. A., Oleinik O. A., “Kraevye zadachi dlya uravnenii s chastnymi proizvodnymi v negladkikh oblastyakh”, UMN, 38:2 (1983), 3–76 | MR | Zbl

[11] Naralenkov M. I., Nekotorye otsenki obobschennykh reshenii bigarmonicheskogo uravneniya, Rukopis dep. v VINITI 4.07.82, No 2804–82 Dep.

[12] Kondratev V. A., Kopachek I., Lekveishvili D. M., Oleinik O. A., “Neuluchshaemye otsenki v prostranstvakh Gëldera i tochnyi printsip Sen-Venana dlya reshenii bigarmonicheskogo uravneniya”, Tr. MIAN, 166, 1984, 91–106 | MR | Zbl

[13] Kondratev V. A., Oleinik O. A., “Neuluchshaemye otsenki v prostranstvakh Gëldera dlya obobschennykh reshenii bigarmonicheskogo uravneniya, sistemy uravnenii Nave–Stoksa i sistemy Karmana v negladkikh dvumernykh oblastyakh”, Vestn. MGU. Ser. matem., mekh., 1983, no. 6, 22–39 | MR | Zbl

[14] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl

[15] Fikera G., Teoremy suschestvovaniya v teorii uprugosti, Mir, M., 1974

[16] Agmon S., Duglis A., Nirenberg L., Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, IL, M., 1962