Ahmed T. M. On Ideals and alpha-Sets in Topological Spaces with Applications to Boundary Values Issues in (ε,δ)-Domains
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Abstract
In order to handle mixed boundary value issues inside local domains of the (ε,δ) type, which permit more complicated geometries than classical domains, this study introduces a novel framework based on ideals and α-sets in topological spaces. Intrinsic features of these domains are extracted, boundary trace, extension, and interpolation theorems are established, and these theorems are then used to solve mixed boundary value issues. Additionally, we investigate the behavior of Bessel and Besov potential spaces on these domains using a novel case: partially disappearing traces on Ahlfors regular sets. This allows us to go beyond the existing findings in smooth spaces.
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