On compactness of classes of solutions of the Dirichlet problem with restrictions of the theoretics-set type

2020/11/09 by O. P. Dovhopiatyi, Evgeny Sevost’yanov, Dovhopiatyi, O. P. +1
Mathematics · #30C62 #30C65 #30C75 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2011.04768

openalex publication_date 2020/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We have proved theorems on compact classes of homeomorphisms with hydrodynamic normalization that are solutions of the Beltrami equation, whose characteristics are compactly supported and satisfy certain constraints of the theoretical-set type. As a consequence, we obtained results on compact classes of solutions of corresponding Dirichlet problems considered in some Jordan domain.

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