Solutions of the Loewner equation with combined driving functions

@article{Prokhorov2021SolutionsOT,
  title={Solutions of the Loewner equation with combined driving functions},
  author={Dmitri Prokhorov and Andrey Zakharov and Andrey Zherdev},
  journal={Izvestia of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics},
  year={2021}
}
The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to the Loewner equations with piecewise constant driving functions and with combined constant and square root driving functions. In both cases, there is an analytical and geometrical description of generated traces. 
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References

SHOWING 1-9 OF 9 REFERENCES

Exact Solutions for Loewner Evolutions

In this note, we solve the Loewner equation in the upper half-plane with forcing function ξ(t), for the cases in which ξ(t)has a power-law dependence on time with powers 0, 1/2, and 1. In the first

Integrability of a Partial Case of the Lowner Equation

Perturbation of the tangential slit by conformal maps

Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I

ON TANGENTIAL SLIT SOLUTION OF THE LOEWNER EQUATION

For a non-tangential slit (t), the behavior of the driving function �(t) near zero in the Loewner equation is well understood; for tangential slit, the situation is less clear. In this paper, we

Conformally Invariant Processes in the Plane

Theoretical physicists have predicted that the scaling limits of many two-dimensional lattice models in statistical physics are in some sense conformally invariant. This belief has allowed physicists

A Sharp Condition for the Loewner Equation to Generate Slits

D. Marshall and S. Rohde have recently shown that there exists C 0 > 0 so that the Loewner equation generates slits whenever the driving term is Holder continuous with exponent ½ and norm less than C

Singular and tangent slit solutions to the Lowner equation

We consider the Lowner differential equation generating univalent maps of the unit disk (or of the upper half-plane) onto itself minus a single slit. We prove that the circular slits, tangent to the

Exact solutions of the Loewner equation

  • Anal. Math. Phys. 10,
  • 2020