Univalence and holomorphic extension of the solution to \(\omega\)-controlled Loewner-Kufarev equations. (English) Zbl 1441.93118
Summary: We prove that a solution to the \(\omega\)-controlled Loewner-Kufarev equation, which was introduced by the first two authors, exists uniquely, is univalent and starlike on the unit disk and can be extended holomorphically across the unit circle.
MSC:
| 93C20 | Control/observation systems governed by partial differential equations |
| 30C99 | Geometric function theory |
| 35C10 | Series solutions to PDEs |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
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