Geodesic
Maximal functions and the Dirichlet problem in the class of $m$-convex functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 519-527

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In this work, we introduce the concept of maximal $m$-convex $(m-cv)$ functions and we solve the Dirichlet Problem with a given continuous boundary function for strictly $m$-convex domains $D\subset {\mathbb R}^{n} $. We prove that for the solution of the Dirichlet problem in the class of $m-cv$ functions its Hessian $H_{\omega }^{n-m+1} =0$ in the domain $D$.
Keywords: subharmonic functions, convex functions, $m$-convex functions, Borel measures, Hessians. 
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     author = {Azimbay Sadullaev and Rasulbek Sharipov},
     title = {Maximal functions and the {Dirichlet} problem in the class of $m$-convex functions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
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     number = {4},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2024_17_4_a10/}
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Azimbay Sadullaev; Rasulbek Sharipov. Maximal functions and the Dirichlet problem in the class of $m$-convex functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 519-527. http://geodesic.mathdoc.fr/item/JSFU_2024_17_4_a10/