An \({L^p}\) inhomogeneous polyharmonic Neumann problem on Lipschitz domains in \({\mathbb{R}^n}\). (Chinese. English summary) Zbl 1463.31006
Summary: In this paper, we study an inhomogeneous polyharmonic Neumann problem with \({L^p}\) boundary data on Lipschitz domains in \({\mathbb{R}^n}\) by the method of layer potentials. Applying multilayer \(S\)-potentials, which are higher order analogues of the classical singular layer potential and defined in terms of polyharmonic fundamental solutions, the unique integral representation solution is given for the inhomogeneous polyharmonic Neumann problem on Lipschitz domains in \({\mathbb{R}^n}\) when the boundary data are in some \({L^p}\) spaces.
MSC:
31B10 | Integral representations, integral operators, integral equations methods in higher dimensions |
31B30 | Biharmonic and polyharmonic equations and functions in higher dimensions |
35J40 | Boundary value problems for higher-order elliptic equations |