Construction in a piecewise smooth domain of a function of the class H2 from the value of the conormal derivative

Abstract

The problem of the construction in a bounded domain Ω ⊂ ℝm with a Lipschitz boundary of a function Φ ∃ H2(Ω), for which the conormal derivative on ∂Ω coincides with the normal component of a given vector field u ∃ H1(Ω, C3), is discussed. The solution of this problem is given for piecewise smooth boundaries in the case m=3. © 1990 Plenum Publishing Corporation.