On Hölder Continuity of Solutions to the Beltrami Equations

被引：0

作者：

Ryazanov, V. ^{[1
,2
]}

Salimov, R. ^{[3
]}

Sevost'yanov, E. ^{[4
,5
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Appl Math & Mech, Slavyansk, Donetsk Oblast, Ukraine

[2] B Khmelnytskyi Cherkasy Natl Univ, Cherkassy, Ukraine

[3] Natl Acad Sci Ukraine, Inst Math, Kiev, Ukraine

[4] I Franko Zhytomyr State Univ, Zhytomyr, Ukraine

[5] Natl Acad Sci Ukraine, Inst Appl Math & Mech, Slavyansk, Donetsk Oblast, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2023年 / 75卷 / 04期

关键词：

D O I：

10.1007/s11253-023-02218-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the problem of local behavior of solutions to the Beltrami equations in arbitrary domains and establish sufficient conditions for the complex coefficient of the Beltrami equation guaranteeing the existence of its Holder-continuous solution in an arbitrary domain. These results can be used both for the investigation of boundary-value problems for the Beltrami equation and in the problems of hydromechanics of strongly anisotropic and inhomogeneous media.

引用

页码：586 / 599

页数：14

共 50 条

[31] Hölder Continuous Solutions of Active Scalar Equations
Isett P.
Vicol V.
Annals of PDE, 1 (1)
[32] On Harnack inequality and Hölder continuity for non uniformly elliptic equations
Di Fazio, Giuseppe
Mamedov, Farman
RICERCHE DI MATEMATICA, 2024, : 271 - 300
[33] A New Unified Method for Boundary Hölder Continuity of Parabolic Equations
Ding, Mengyao
Zhang, Chao
JOURNAL OF GEOMETRIC ANALYSIS, 2024, 34 (06)
[34] Hlder Continuity of the Gradient of Solutions of Nonlinear Degenerate Parabolic Systems
陈亚渐
ActaMathematicaSinica, 1986, (04) : 309 - 331
[35] Hlder Continuity of the Gradient of Solutions of Nonlinear Degenerate Parabolic Systems
陈亚渐
Acta Mathematica Sinica,English Series, 1986, (04) : 309 - 331
[36] Local Hölder continuity of weak solutions for an anisotropic elliptic equation
Agnese Di Castro
Nonlinear Differential Equations and Applications NoDEA, 2013, 20 : 463 - 486
[37] Logarithmic Hölder continuous mappings and Beltrami equation
Evgeny Sevost’yanov
Sergei Skvortsov
Analysis and Mathematical Physics, 2021, 11
[38] Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group
Maria Manfredini
Giampiero Palatucci
Mirco Piccinini
Sergio Polidoro
The Journal of Geometric Analysis, 2023, 33
[39] Existence of Solutions for Some Nonlinear Elliptic Equations in Musielak Spaces with Only the Log-Hölder Continuity Condition
Mustafa Ait Khellou
Sidi Mohamed Douiri
Youssef El Hadfi
Mediterranean Journal of Mathematics, 2020, 17
[40] Hölder continuity and Harnack estimate for non-homogeneous parabolic equations
Arya, Vedansh
Julin, Vesa
MATHEMATISCHE ANNALEN, 2025, 391 (02) : 2319 - 2335

← 1 2 3 4 5 →