BMO and Dirichlet Problem for Degenerate Beltrami Equation

被引：0

作者：

Gutlyanskii V. ^{[1
]}

Ryazanov V. ^{[1
,2
]}

Sevost’yanov E. ^{[3
]}

Yakubov E. ^{[4
]}

机构：

[1] Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk

[2] Bogdan Khmelnytsky National University of Cherkasy, Lab. of Math. Phys., Cherkasy

[3] Zhytomyr Ivan Franko State University, Zhytomyr

[4] Holon Institute of Technology, Holon

来源：

Journal of Mathematical Sciences | 2022年 / 268卷 / 2期

关键词：

BMO; bounded mean oscillation; degenerate Beltrami equations; Dirichlet problem; finite mean oscillation; FMO; hydromechanics (fluid mechanics); potential theory;

D O I：

10.1007/s10958-022-06189-w

中图分类号：

学科分类号：

摘要：

Following Bojarski and Vekua, we have studied the Dirichlet problem limz→ζRef(z)=φ(ζ) as z → ζ, z ∈ D, ζ ∈ ∂D, with continuous boundary data φ(ζ) in bounded domains D of the complex plane ℂ, where f satisfies the degenerate Beltrami equation fz¯=μ(z)fz,|μ(z)|<1, a.e. in D. Assuming that D is an arbitrary simply connected domain, we have established, in terms of μ, the BMO and FMO criteria, as well as a number of other integral criteria, on the existence and representation of regular discrete open solutions to the stated above problem. We have also proven similar theorems on the existence of multivalued solutions to the problem with single-valued real parts in an arbitrary bounded domain D with no boundary component degenerated to a single point. Finally, we have given a similar solvability and representation results concerning the Dirichlet problem in such domains for the degenerate A-harmonic equation associated with the Beltrami equation. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：157 / 177

页数：20

共 52 条

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