@article{Khidr2025, 
author = {Shaban Khidr and Salomon Sambou},
title = {L    p  -theory for the        ∂        ∂    ¯  -equation and isomorphisms results},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {1},
pages = {68-86},
keywords = {∂∂¯-problem, distributional boundary values, extensible currents, regularizing operators},
url = {https://www.sciopen.com/article/10.3934/era.2025004},
doi = {10.3934/era.2025004},
abstract = {We establish an        L          l      o      c              p      -existence theorem for the        ∂        ∂    ¯  -equation on a half-space of              C        n  . The result is achieved for forms of class        L          l      o      c              p       as well as for those forms in the scale of        W          l      o      c              1      ,      p      -Sobolev spaces and admitting distributional boundary values. Some isomorphisms and regularity results in relation to de Rham, Bott–Chern, and Aeppli cohomology groups are moreover obtained.}
}