Surjectivity of tangential trace operators on fractal-boundary extension domains

Establish the surjectivity of the tangential trace operators defined on the relevant H(curl)-type spaces for bounded H^1-extension domains with fractal boundaries, thereby enabling the complete resolution of Maxwell's equations on such domains.

Background

The paper develops generalized normal and tangential trace operators for bounded H^1-extension domains, including domains with fractal boundaries such as the Koch snowflake. Although the authors establish a rigorous abstract trace theory and prove weak well-posedness for certain boundary-value problems, the surjectivity of the tangential trace operators from the relevant H(curl)-type spaces remains unresolved for fractal geometries. This unresolved surjectivity obstructs the direct completion of the Maxwell boundary-value theory in the non-Lipschitz setting, so the full resolution of Maxwell's equations is deferred to future work.