LINEAR ELASTICITY IN 3-DIMENSIONAL LIPSCHITZ DOMAINS

Abstract. We study the Green’s function of the linear elasticity in a three dimensional bounded Lipschitz domain Ω. Our main results assert that if G is Green’s function of the linear elasticity, then |G(X,Y) | ≤ c 1|X−Y | and |G(X,Y) | ≤ cmin(dist(X,∂Ω),dist(Y,∂Ω))η|X−Y |1+η for some η> 0 and for all X,Y ∈ Ω. For its application, we deduce Lp(Ω) estimate of solutions of inhomogeneous elasticity equations and show the solvability of elasticity equations with bound-ary data B1α(∂Ω). 1