# Duality dispute for elliptic regularity Answer

Hello expensive customer to our community We will proffer you an answer to this query Duality dispute for elliptic regularity ,and the respond will breathe typical by documented data sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning concerning the respond to this query.

Duality dispute for elliptic regularity

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 $$p>3$$. (See Corollary 3.10.) Then the writer states (Remark 3.11):

By a duality dispute it’s simple to infer from earlier assertion that the Laplace operator [between $$W^1_p$$ and $$(W^1_{p’})^*$$] is an isomorphism […] when $$3/2-epsilon for a $$epsilon > 0$$.

What is “a duality argument” and which theorem ought to breathe used on this illustration?

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

we are going to proffer you the answer to Duality dispute for elliptic regularity query through our community which brings all of the solutions from a number of dependable sources.