Resolution and optimal regularity for a biharmonic equation with impedance boundary conditions and some generalizations

Abstract

In this work, a biharmonic equation with an impedance (non standard) boundary condition and more general equations are considered. The study isperformed in the space $L^{p}(-1,0$ $;$ $X)$, $1 0}$ set in a domain having a thin layer. The limiting problem models, for instance, the bending of a thin plate with a stiffness on a part of its boundary (see Favini et al. [13]). We build an explicit representation of the solution, then we study its regularity and give a meaning to the non standard boundary condition.