Logharmonic mappings on linearly connected domains
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DOI: 10.1007/s13324-019-00318-6
Abstract: A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation $$\dfrac{\overline{f_{ \overline{z}}}}{\overline{f}}=a\dfrac{f_{z}}{f}$$fz¯¯f¯=afzf. In this paper we investigate the univalence of logharmonic mappings of the form $$ f=zH\overline{G},$$f=zHG¯,… read more here.
Keywords: linearly connected; univalence; connected domains; logharmonic mappings ... See more keywords
A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane
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DOI: 10.1016/j.jmaa.2018.04.045
Abstract: Abstract A new proof is given of a simple probabilistic lemma which implies the solution of the Dirichlet problem for simply connected domains in the plane. This proof uses the conformal invariance of planar Brownian… read more here.
Keywords: dirichlet problem; domains plane; solution dirichlet; connected domains ... See more keywords
Magnetic helicity in multiply connected domains
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DOI: 10.1017/s0022377819000576
Abstract: Magnetic helicity is a fundamental quantity of magnetohydrodynamics that carries topological information about the magnetic field. By ‘topological information’, we usually refer to the linkage of magnetic field lines. For domains that are not simply… read more here.
Keywords: helicity multiply; multiply connected; topology; connected domains ... See more keywords