Mixed Riemann-Hilbert boundary value problem with simply connected fibersČerne, Miran (Avtor) boundary value problemsmixed Riemann-Hilbert problemCherepanov problemWe 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 $\partial\Delta\setminus\mathring{L}$.20242024-02-15 13:42:47Neznano18182sl