Determine Sobolev interpolation norm-equivalence constants on general domains

Determine the norm-equivalence constants in the identification of fractional Sobolev spaces with real interpolation spaces on suitable general domains, including their dependence on the domains and the associated extension operators.

Background

On the torus, the paper establishes an isometric identification between the fractional Sobolev space H^s and the real interpolation space between L^2 and an integer-order Sobolev space. For general domains, such as bounded Lipschitz domains, the corresponding spaces are generally identified only up to equivalence of norms.

The constants in this norm equivalence depend on the domain and on the associated extension operators. The paper explicitly notes that these constants are not known in general, leaving their determination as an unresolved problem relevant to obtaining explicit operator and approximation bounds on non-periodic domains.