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@article{JSFU_2025_18_3_a10, author = {Azimbay Sadullaev and Rasulbek Sharipov and Mukhiddin Ismoilov}, title = {$m-cv$ measure $\omega ^{*} (x,E,D)$ and condenser capacity $C(E,D)$ in the class $m$-convex functions}, journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika}, pages = {387--401}, publisher = {mathdoc}, volume = {18}, number = {3}, year = {2025}, language = {en}, url = {http://geodesic.mathdoc.fr/item/JSFU_2025_18_3_a10/} }
TY - JOUR AU - Azimbay Sadullaev AU - Rasulbek Sharipov AU - Mukhiddin Ismoilov TI - $m-cv$ measure $\omega ^{*} (x,E,D)$ and condenser capacity $C(E,D)$ in the class $m$-convex functions JO - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika PY - 2025 SP - 387 EP - 401 VL - 18 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/JSFU_2025_18_3_a10/ LA - en ID - JSFU_2025_18_3_a10 ER -
%0 Journal Article %A Azimbay Sadullaev %A Rasulbek Sharipov %A Mukhiddin Ismoilov %T $m-cv$ measure $\omega ^{*} (x,E,D)$ and condenser capacity $C(E,D)$ in the class $m$-convex functions %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2025 %P 387-401 %V 18 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/JSFU_2025_18_3_a10/ %G en %F JSFU_2025_18_3_a10
Azimbay Sadullaev; Rasulbek Sharipov; Mukhiddin Ismoilov. $m-cv$ measure $\omega ^{*} (x,E,D)$ and condenser capacity $C(E,D)$ in the class $m$-convex functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 3, pp. 387-401. http://geodesic.mathdoc.fr/item/JSFU_2025_18_3_a10/
[1] B.Abdullaev, A.Sadullaev, “Potential theory in the class of $m$-subharmonic functions. Analytic and geometric issues of complex analysis”, Trudy Mat. Inst. Steklova, 279, MAIK Nauka/Interperiodica, M., 2012, 155–180 | DOI | MR
[2] Akademie Verlag, Berlin, 1955 | MR
[3] A.D.Aleksandrov, “Dirichlet's problem for the equation $\det (z_{ij} )=\varphi$”, Vestnic Leningrad University, 13 (1958), 5–24 (in Russian) | MR
[4] I.J.Bakelman, “Variational problems and elliptic Monge-Ampere equations”, J. Diff. Geo, 18 (1983), 669–999 | MR
[5] I.J.Bakeman, Convex Analysis and Nonlinear Geometric Elliptic Equations, Springer-Verlag, Berlin, 1994 | DOI | MR
[6] Z.Błocki, “Weak solutions to the complex Hessian equation”, Ann.Inst. Fourier, Grenoble, 5 (2005), 1735–1756 | DOI | MR
[7] M.Brelot, Éléments de la théorie classique du potentiel, Les Cours de Sorbonne, 3, Centre de Documentation Universitaire, Paris, 1959 | MR
[8] K.S.Chou, X.J.Wang, “Variational theoryfor Hessian equations”, Comm. Pure Appl. Math., 54 (2001), 1029–1064 | DOI | MR
[9] S.Dinew, S.Kolodziej, “A priori estimates for the complex Hessian equation”, Anal. PDE, 7 (2014), 227–244 | DOI | MR
[10] S. Dinew, S.Kolodziej, “Non standard properties of $m$-subharmonic functions”, Dolom. Res. Not. Approx., 11 (2018), 35–50 | MR
[11] N.Ivochkina, N.S.Trudinger, X.J.Wang, “The Dirichlet problem for degenerate Hessian equations”, Comm. Partial Diff. Equations, 29 (2004), 219–235 | DOI | MR
[12] N.S.Landkof, Foundations of Modern Potential Theory, Springer, Berlin–Heidelberg, 1972 | MR
[13] S.Y.Li, “On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian”, Asian J.Math., 8 (2004), 87–106 | DOI | MR
[14] C.H.Lu, “A variational approach to complex Hessian equations in ${\mathbb C}^{n} $”, Journal of Mathematical Analysis and Applications, 431:1 (2015), 228–259 | DOI | MR
[15] H.Ch.Lu, “Solutions to degenerate Hessian equations”, Journal de Mathematique Pures et Appliques, 100:6 (2013), 785–805 | DOI | MR
[16] A.Sadullaev, “Definition of Hessians for $m$-convex functions as Borel measures”, Analysis and Applied Mathematics, AAM 2022, Trends in Mathematics, 6, Birkhauser, Cham, 2024, 13–19 | DOI | MR
[17] A.Sadullaev, Potential theory, Universitet, Tashkent, 2022 (in Russian)
[18] R.A.Sharipov, M.B.Ismoilov, “$m$-convex $(m-cv)$ functions”, Azerbaijan Journal of Mathematics, 13:2 (2023), 237–247 | DOI | MR
[19] N.S.Trudinger, X.J.Wang, “Hessian measures I”, Topological Methods in Nonlinear Analysis, 10:2 (1997), 225–239 | DOI | MR
[20] N.S.Trudinger, X.J.Wang, “Hessian measures II”, Anal. Math., 150 (1999), 579–604 | MR
[21] N.S.Trudinger, X.J.Wang, “Hessian measures III”, J. Funct. Anal., 193 (2002), 1–23 | DOI | MR