Maximal Functions and the Dirichlet Problem in the Class of m-convex Functions

Maximal Functions and the Dirichlet Problem in the Class of m-convex Functions

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 ⊂ R n . We prove that for the solution of the Dirichlet problem in the class m − cv of functions, its Hessian Hn−...

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Veröffentlicht in:Journal of Siberian Federal University. Mathematics & Physics 2024-10, Vol.17 (4), p.519-527
Hauptverfasser: Sadullaev, Azimbay, Sharipov, Rasulbek
Format: Artikel
Sprache:eng
Schlagworte:
Continuity (mathematics)
Convex analysis
Dirichlet problem
Domains
Eigenvalues
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Zusammenfassung: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 ⊂ R n . We prove that for the solution of the Dirichlet problem in the class m − cv of functions, its Hessian Hn−m+1 ω = 0 in the domain D.
ISSN:1997-1397
2313-6022