| Title: | Mixed Riemann-Hilbert boundary value problem with simply connected fibers |
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| Authors: | ID Černe, Miran (Author) |
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| Files: |  URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0022247X23005607
 PDF - Presentation file, download (467,68 KB)
MD5: F3FD0AE1DB8793DE5E649ED22CB0486D
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | We study the existence of solutions of mixed Riemann-Hilbert or Cherepanov boundary value problem with simply connected fibers on the unit disk $\Delta$. Let ▫$L$▫ be a closed arc on $\partial\Delta$ with the end points $\omega_{-1}, \omega_1$ and let $a$ be a smooth function on $L$ with no zeros. Let $\{\gamma_{\xi}\}_{\xi\in\partial\Delta\setminus\mathring{L}}$ be a smooth family of smooth Jordan curves in $\mathbb C$ which all contain point $0$ in their interiors and such that $\gamma_{\omega_{-1}}$, $\gamma_{\omega_{1}}$ are strongly starshaped with respect to $0$. Then under condition that for each $w\in \gamma_{\omega_{\pm 1}}$ the angle between $w$ and the normal to $\gamma_{\omega_{\pm 1}}$ at $w$ is less than $\frac{\pi}{10}$, there exists a Hölder continuous function $f$ on $\overline{\Delta}$, holomorphic on $\Delta$, such that ${\rm Re}(\overline{a(\xi)} f(\xi)) = 0$ on $L$ and $f(\xi)\in\gamma_{\xi}$ on $\partial\Delta\setminus\mathring{L}$. |
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| Keywords: | boundary value problems, mixed Riemann-Hilbert problem, Cherepanov problem |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 04.07.2023 |
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| Year of publishing: | 2024 |
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| Number of pages: | 20 str. |
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| Numbering: | Vol. 529, iss. 1, art. no. 127557 |
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| PID: | 20.500.12556/DiRROS-18182  |
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| UDC: | 517.9 |
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| ISSN on article: | 0022-247X |
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| DOI: | 10.1016/j.jmaa.2023.127557 |
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| COBISS.SI-ID: | 158869763 |
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| Note: |
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| Publication date in DiRROS: | 15.02.2024 |
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| Views: | 965 |
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| Downloads: | 499 |
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| Metadata: |    |
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