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@article{VSGTU_2011_1_a7, author = {A. K. Gushchin}, title = {The estimates of the solution of the {Dirichlet} problem with boundary function from $L_p$ for a~second-order elliptic equation}, journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences}, pages = {53--67}, publisher = {mathdoc}, number = {1}, year = {2011}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a7/} }
TY - JOUR AU - A. K. Gushchin TI - The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a~second-order elliptic equation JO - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences PY - 2011 SP - 53 EP - 67 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a7/ LA - ru ID - VSGTU_2011_1_a7 ER -
%0 Journal Article %A A. K. Gushchin %T The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a~second-order elliptic equation %J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences %D 2011 %P 53-67 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a7/ %G ru %F VSGTU_2011_1_a7
A. K. Gushchin. The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a~second-order elliptic equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 53-67. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a7/
[1] Mikhailov V. P., “The Dirichlet problem for a second order elliptic equation”, Differenc. Uravneniya, 12:10 (1976), 1877–1891 | MR
[2] Gushchin A. K., “On the Dirichlet problem for a second-order elliptic equation”, Math. USSR-Sb., 65:1 (1990), 19–66 | DOI | MR | Zbl
[3] Gushchin A. K., Mikhailov V. P., “On solvability of nonlocal problems for a second-order elliptic equation”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 101–136 | DOI | MR
[4] Gushchin A. K., “Some properties of the solutions of the Dirichlet problem for a second-order elliptic equation”, Sb. Math., 189:7 (1998), 1009–1045 | DOI | DOI | MR | Zbl
[5] Gushchin A. K., “On the interior smoothness of solutions to second-order elliptic equations”, Siberian Math. J., 46:5 (2005), 826–840 | DOI | MR | Zbl
[6] Gushchin A. K., “A strengthening of the interior Hölder continuity property for solutions of the Dirichlet problem for a second-order elliptic equation”, Theoret. and Math. Phys., 157:3 (2008), 1655–1670 | DOI | DOI | MR | Zbl
[7] Gushchin A. K., Mikhailov V. P., “On the existence of boundary values for solutions of elliptic equations”, Vestn. Sam. Gos. Un-ta. Estestvennonauchn. Ser., 2008, no. 8/1(67), 76–94
[8] Carleson L., “An interpolation problem for bounded analytic functions”, Amer. J. Math., 80:4 (1958), 921–930 | DOI | MR | Zbl
[9] Carleson L., “Interpolation by bounded analytic functions and the corona problem”, Ann. of Math., 76:3 (1962), 547–559 | DOI | MR | Zbl
[10] Hörmander L., “$L^p$-estimates for (pluri-) subharmonic functions”, Math. Scand., 20 (1967), 65–78 | MR | Zbl
[11] Gushchin A. K., Mikhailov V. P., “On the continuity of the solutions of a class of non-local problems for an elliptic equation”, Sb. Math., 186:2 (1995), 197–219 | DOI | MR | Zbl
[12] Gushchin A. K., “A condition for the compactness of operators in a certain class and its application to the analysis of the solubility of non-local problems for elliptic equations”, Sb. Math., 193:5 (2002), 649–668 | DOI | DOI | MR | Zbl
[13] Gushchin A. K., Mikhailov V. P., “On the existence of boundary values of solutions of an elliptic equation”, Math. USSR-Sb., 73:1 (1992), 171–194 | DOI | MR | Zbl
[14] Guščin A. K., Mihaĭlov V. P., “On boundary values in $ L_p$, $ p > 1$, of solutions of elliptic equations”, Math. USSR-Sb., 36:1 (1980), 1–19 | DOI | MR
[15] Petrushko I. M., “On boundary values in $ \mathscr{L}_p$, $ p>1$, of solutions of elliptic equations in domains with A. Lyapunov boundary”, Math. USSR-Sb., 48:2 (1984), 565–585 | DOI | MR | Zbl | Zbl
[16] Mikhailov V. P., “Boundary values in $L_p$, $p>1$, of solutions of a second-order linear elliptic equation”, Differenc. Uravneniya, 19:2 (1983), 318–337 | MR
[17] Alkhutov Yu. A., Kondrat'ev V. A., “Solvability of the Dirichlet problem for second-order elliptic equations in a convex domain”, Differential Equations, 28:5 (1992), 650–662 | MR
[18] De Giorgi E., “Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari”, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 3:3 (1957), 25–43 | MR | Zbl
[19] Nash J., “Continuity of solutions of parabolic and elliptic equations”, Amer. J. Math., 80:4 (1958), 931–954 | DOI | MR | Zbl
[20] Moser J., “A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations”, Comm. Pure Appl. Math., 13:3 (1960), 457–468 | DOI | MR | Zbl
[21] Ladyzhenskaya O. A., Uraltseva N. N., Linear and quasilinear equations of elliptic type, Nauka, Moscow, 1973, 576 pp. | MR
[22] Gilbarg D., Trudinger N. S., Elliptic partial differential equations of second order, Fundamental Principles of Mathematical Sciences, 224, Springer-Verlag, Berlin, 1983, 513 pp. ; Gilbarg D. Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989, 464 pp. | MR | Zbl | MR | Zbl
[23] Mikhailov V. P., Gushchin A. K., “Additional chapters of course “Equations of Mathematical Physics””, Lekts. Kursy NOC, 7, Steklov Math. Inst., RAS, Moscow, 2007, 3–144 | DOI
[24] Maz'ya V. G., “On a degenerating problem with directional derivative”, Math. USSR-Sb., 16:3 (1972), 429–469 | DOI | Zbl