Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains
We establish the well-posedness of the inhomogeneous Dirichlet problem for Δ2 in arbitrary Lipschitz domains in R3, with data from Besov-Triebel-Lizorkin spaces, for the optimal range of indices. The main novel contribution is to allow for certain nonlocally convex spaces to be considered, and to establish integral representations for the solution.
Mitrea, Irina, Marius Mitrea, and Matthew Wright. "Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains." Journal of Mathematical Sciences 172, no. 1 (2011): 24-134.
Journal of Mathematical Sciences