Resolution and Optimal Regularity for a Biharmonic Equation with Impedance Boundary Conditions and Some Generalizations
Résumé
In this work, a biharmonic equation with an impedance (non standard) boundary condition and more general equations are considered. The study is performed in the space L^{p}(-1,0 ; X), 10} 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. We build an explicit representation of the solution, then we study its regularity and give a meaning to the non standard boundary condition.