Singular boundary conditions and regularity for the biharmonic problem in the half-space (Q2480617)

The authors are interested in the following boundary value problem for the biharmonic operator (denoted by (P)) \[ \begin{alignedat}{2} \Delta^2 u &= f \quad&&\text{in }\mathbb R^N_+,\\ u &= g_0 \quad&&\text{on }\Gamma =\mathbb R^{N-1},\\ \partial_N u &= g_1 \quad&&\text{on }\Gamma=\mathbb R^{N-1}. \end{alignedat} \] The authors investigate the regularity of generalized solutions of the problem in weighted Sobolev spaces, then they consider also the case of singular boundary conditions. Also the case of other sorts of boundary conditions is envisaged.