Boundary behavior and the Dirichlet problem for Beltrami equations

DOI10.1090/S1061-0022-2014-01308-8zbMath1302.30050OpenAlexW1977544707MaRDI QIDQ2931153

D. A. Kovtonyuk, I. V. Petkov, Ruslan Radikovich Salimov, Vladimir I. Ryazanov

Publication date: 24 November 2014

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2014-01308-8

zbMATH Keywords

Dirichlet problemboundary behaviorBeltrami equation

Mathematics Subject Classification ID

Boundary value problems in the complex plane (30E25) Quasiconformal mappings in the complex plane (30C62) First-order elliptic systems (35J46)

Related Items (20)

The lower \(Q\)-homeomorphisms relative to a \(p\)-modulus ⋮ Toward the theory of Orlicz–Sobolev classes ⋮ The Schwartz inequality and the Schwartz formula for \(A\)-analytic functions ⋮ Prime ends in the mapping theory on the Riemann surfaces ⋮ Lower estimates for $p$-moduli and Sobolev class mappings ⋮ On the boundary behavior of mappings in the class \(W^{1,1}_{\mathrm{loc}}\) on Riemann surfaces ⋮ Generalized quasi-isometries on smooth Riemannian manifolds ⋮ Robin boundary-value problem for the Beltrami equation ⋮ On divergence-type linear and quasi-linear equations in the complex plane ⋮ On recent advances in boundary-value problems in the plane ⋮ On compact classes of Beltrami solutions and Dirichlet problem ⋮ The Beltrami equations and prime ends ⋮ On compact classes of solutions of Dirichlet problem in simply connected domains ⋮ On the Hölder property of mappings in domains and on boundaries ⋮ On the local properties of solutions of the nonlinear Beltrami equation ⋮ On the compactness of classes of the solutions of the Dirichlet problem ⋮ Prime ends and Orlicz–Sobolev classes ⋮ To the theory of mappings of the Sobolev class with the critical index ⋮ Prime ends in theory of mappings with finite distortion in the plane ⋮ On the boundary behavior of mappings with finite distortion in the plane

Cites Work

• On integral conditions in the mapping theory
• On recent advances in the Beltrami equations
• Extremal length and functional completion
• On ring solutions of Beltrami equations
• On the theory of mappings with finite area distortion
• Quasiextremal distance domains and extension of quasiconformal mappings
• On mappings in the Orlicz--Sobolev classes on Riemannian manifolds
• On the Dirichlet problem for the Beltrami equations in finitely connected domains
• Finite mean oscillation and the Beltrami equation
• Lectures on \(n\)-dimensional quasiconformal mappings
• On regular solutions of the Dirichlet problem for the Beltrami equations
• On extension of some generalizations of quasiconformal mappings to a boundary
• Integral conditions in the theory of the Beltrami equations
• On strong solutions of the Beltrami equations
• Moduli in Modern Mapping Theory
• Rings and Quasiconformal Mappings in Space
• Injectivity theorems in plane and space
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