A Riemann jump problem for biharmonic functions in fractal domains

Abstract

Biharmonic functions are the solutions of the fourth order partial differential equation $$\Delta \Delta \omega =0$$ . The purpose of this paper is to solve a kind of Riemann boundary value problem for biharmonic functions assuming higher order Lipschitz boundary data. We approach this problem making use of generalized Teodorescu transforms for obtaining the explicit expression of its solution in a Jordan domain $$\Omega \subset \mathbb {R}^2$$ with fractal boundary.