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Let Ω be a bounded Lipschitz domain in Rn. We develop a new approach to the invertibility on Lp(∂Ω) of the layer potentials associated with elliptic equations and systems in Ω. As a consequence, for n⩾4 and 2(n−1)(n+1)−ε<p<2 where ε>0 depends on Ω, we obtain the solvability of the Lp Neumann type boundary value problems for second order elliptic systems. The analogous results for the biharmonic...
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