Biharmonic continuations of gradients with the help of monogenic functions with values in the biharmonic algebra

• Date: 2024
• Main Authors: Gryshchuk, S., Грищук, Сергій
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7867
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 Necessary and sufficient conditions are established for the existence of the continuations of gradients of biharmonic functions $u_1$ and $u_2$ across a smooth curve $\Gamma$ ($u_k \colon D_k \longrightarrow \mathbb{R},$ $k=1,2,$ and $\Gamma$ is a common part of the boundaries of $D_1$ and...