Toward the theory of the Dirichlet problem for the Beltrami equations
DOI:
https://doi.org/10.15407/dopovidi2015.11.023Keywords:
Beltrami equations, Dirichlet problem, finitely connected domains, prime ends, pseudoregular and multivalent solutions, regular solutions, simply connected domainsAbstract
The Dirichlet problem for the degenerate Beltrami equations in arbitrary finitely connected domains is studied. In terms of the tangent dilatations, a series of criteria for the existence of regular solutions in arbitrary simply connected domains, as well as pseudoregular and multivalent solutions in arbitrary finitely connected domains without degenerate boundary components, are formulated.
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