Smooth Continuations of Gradients for Biharmonic Functions via Monogenic Functions
Explore a 17-minute conference talk from the HyperComplex Seminar focusing on smooth continuations of gradients for biharmonic functions using monogenic functions with values in biharmonic algebra. Delve into necessary and sufficient conditions for continuing gradients of two biharmonic functions across a smooth curve, which forms a common boundary between two domains. Learn how this continuation defines a gradient of a biharmonic function in the combined domain. Discover a similar method for finding conditions of smooth continuation of gradients only, resulting in k-order smooth properties on the curve. Examine key concepts including biharmonic functions, biharmonic gradients, biharmonic algebra, monogenic functions, and smooth continuation of functions. Gain insights from references to related works by Gryshchuk, Kalaj, Partyka, and Sakan on topics such as quasiconformal harmonic mappings and close to convex domains.