Short Proofs of Explicit Formulas to Boundary Value Problems for Polyharmonic Equations Satisfying Lopatinskii Conditions

This paper deals with Lopatinskii type boundary value problem (bvp) for the (poly) harmonic differential operators. In case of Robin bvp Laplace equation in ball B1 a Green function is constructed cases c>0, c∉−N, where c coefficient front u condition ∂u∂n+cu=f. To do this definite integral must be computed. The latter possible quadratures (elementary functions) several special cases. simple proof construction based on some solutions radial vector field Λu+cu=f. Elliptic problems Δmu=0 are considered and solved Theorem 2. illustrated by many examples Δu=0, Δ2u=0 Δ3u=0 as well additional results from theory spherical functions proposed.