Geodesic
$L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations
Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 1-17
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The Dirichlet problem for second-order divergence-form elliptic equations with coefficients continuous in a closed domain is considered. A necessary and sufficient condition on the boundary of a compact domain ensuring the unique $L_p$-solubility of the problem in question and also a corresponding coercive $L_p$-estimate for all $p>1$ are obtained. 
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Yu. A. Alkhutov. $L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations. Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/SM_1998_189_1_a0/

[1] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. MMO, 16, URSS, M., 1967, 209–292 | MR | Zbl

[2] Grisvard P., Elliptic problems in nonsmooth domains, Pitman Publ., Boston, 1985 | MR | Zbl

[3] Maslennikova V. N., Bogovskii M. E., “Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries”, Rend. Sem. Mat. Fis. Milano, 56 (1986), 125–138 | DOI | MR | Zbl

[4] Kondratev V. A., “O gladkosti resheniya zadachi Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka v okrestnosti rebra”, Differents. uravneniya, 6 (1970), 1831–1843 | MR | Zbl

[5] Verzhbinskii G. M., Mazya V. G., “O zamykanii v $L_p$ operatora zadachi Dirikhle v oblasti s konicheskimi tochkami”, Izv. vuzov. Ser. matem., 1974, no. 6, 8–19 | MR | Zbl

[6] Mazya V. G., Plamenevskii B. A., “$L_p$-otsenki reshenii ellipticheskikh kraevykh zadach v oblastyakh s rebrami”, Tr. MMO, 37, URSS, M., 1978, 49–93 | MR | Zbl

[7] Alkhutov Yu. A., Kondratev V. A., “Razreshimost zadachi Dirikhle dlya ellipticheskikh uravnenii vtorogo poryadka v vypukloi oblasti”, Differents. uravneniya, 28:5 (1992), 806–818 | MR

[8] Alkhutov Yu. A., “O kriterii $L_p$-razreshimosti zadachi Dirikhle dlya divergentnykh ellipticheskikh uravnenii vtorogo poryadka”, UMN, 50:4 (1995), 135

[9] Alkhutov Yu. A., “O $L_p$-razreshimosti zadachi Dirikhle dlya ellipticheskikh uravnenii vtorogo poryadka”, Materialy mezhdunar. konf. i Chebyshëvskikh chtenii, posv. 175-letiyu so dnya rozhd. P. L. Chebyshëva, T. 1, 1996, 19–22

[10] Kondratev V. A., Landis E. M., “Kachestvennaya teoriya lineinykh differentsialnykh uravnenii v chastnykh proizvodnykh vtorogo poryadka”, Itogi nauki i tekhniki. Sovr. problemy matem. Fundam. napr., 32, VINITI, M., 1988, 99–215 | MR

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

[12] Kondratev V. A., Kopachek I., Oleinik O. A., “O nailuchshikh pokazatelyakh Gëldera dlya obobschennykh reshenii zadachi Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka”, Matem. sb., 131:1 (1986), 113–125 | MR

[13] Littman W., Stampacchia G., Weinberger H. F., “Regular points for elliptic equations with discontinuous coefficients”, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 17 (1963), 43–77 | MR | Zbl

[14] Kondratev V. A., “O razreshimosti pervoi kraevoi zadachi dlya silno ellipticheskikh uravnenii”, Tr. MMO, 16, URSS, M., 1967, 209–292 | MR | Zbl

[15] Mazya V. G., Prostranstva S. L. Soboleva, Izd-vo LGU, L., 1985 | MR | Zbl

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

[17] Stein E., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

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