Domain dependence of Sobolev-curl constants and structure of critical curl-curl solutions

This paper investigates intrinsic critical Sobolev-curl constants on bounded domains and the structure of finite-energy solutions to the critical curl-curl equation in R^3. First, for 1< p < 3, we prove that the intrinsic critical p-curl constant on (0, a)\times D is bounded above by a^{p/3} times a