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elliptic pde – Duality dispute Answer

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elliptic pde – Duality dispute

M. Dauge proved in [1] the regularity property $Delta u in (W^1_p)^*$ $Rightarrow$ $u in W^1_p$ for Dirichlet and Neumann downside in domains with piecewise flush boundaries, for $p>3$. (behold Corollary 3.10). Then the creator acknowledged: “By a duality argument it is easy to deduce from previous statement that the Laplace operator… is an isomorphism …. when $3/2-epsilon <p<3+epsilon$ (see Rematk 3.11). What is “a duality argument” and which theorem must be used on this illustration?

[1] Dauge, M. Neumann and combined issues on curvilinear polyhedra.
Integral Equations Operator Theory 15 (1992), no. 2, 227–261.

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