Vladimir G. Maz'ya, Jürgen Roßmann
Point estimates for Green's matrix to boundary problems for second order elliptic systems in a polyhedral cone
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
35J25 Boundary value problems for second-order, elliptic equations
35J55 Boundary value problems for elliptic systems
35C15 Integral representations of solutions of PDE
35Q72 Other equations from mechanics
Abstract: In this paper we are concerned with boundary value problems
for general second order elliptic equations and systems in a polyhedral cone.
We obtain point estimates of Green's matrix in different areas of the cone. The proof of
these estimates is essentially based on weighted $L_2$ estimates for weak solutions and
their derivatives.
As examples, we consider the Neumann problem to the Laplace equation and the Lam\'e system.
Keywords: Boundary value problems for second-order, elliptic equations, elliptic systems, PDE, equations from mechanics