On compact classes of Beltrami solutions and Dirichlet problem
Oleksandr Dovhopiatyi, Evgeny Sevost’yanov
Abstract
This article is devoted to the study of the problem of compactness of solutions of the differential Beltrami equation with degeneration. We study the case when the complex characteristic of the equations satisfies the constraints of integral type. In this case, we have proved a theorem on the compactness of the class of homeomorphic solutions of the Beltrami equation, which satisfy the hydrodynamic normalization condition at infinity. Another important result is the compactness theorem for the class of open discrete solutions of the Dirichlet problem for the Beltrami equations in the Jordan domain, the imaginary part of which vanishes at some predetermined inner point.
Topics & Concepts
MathematicsCompact spaceDirichlet problemMathematical analysisNormalization (sociology)Dirichlet distributionClass (philosophy)Integral equationPure mathematicsDirichlet integralInfinityDirichlet's energyBoundary value problemSociologyArtificial intelligenceAnthropologyComputer scienceAnalytic and geometric function theoryDifferential Equations and Boundary ProblemsHolomorphic and Operator Theory