20.500.12556/DiRROS-18182 Mixed Riemann-Hilbert boundary value problem with simply connected fibers 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 $\partial\Delta\setminus\mathring{L}$. boundary value problems mixed Riemann-Hilbert problem Cherepanov problem robni problem mešani Riemann-Hilbertov problem problem Čerepanova true false true Angleški jezik Slovenski jezik Neznano 2024-02-15 13:42:47 2024-02-15 13:42:48 2024-02-19 13:44:16 0000-00-00 00:00:00 2024 0 0 20 str. iss. 1, art. no. 127557 Vol. 529 Jan. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-07-04 517.9 0022-247X 10.1016/j.jmaa.2023.127557 158869763 https://www.sciencedirect.com/science/article/pii/S0022247X23005607 1 58fc5773-cbf7-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24692 1-s2.0-S0022247X23005607-main.pdf 1-s2.0-S0022247X23005607-main.pdf 1 F3FD0AE1DB8793DE5E649ED22CB0486D 010105db0127a31c7f4c7564c7ae586b5db0eef0aaef0ac410d643b69a6bb8e1 7c008e10-cbf9-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24693 Inštitut za matematiko, fiziko in mehaniko 0 0 0