Resumen de The Dirichlet problem in domains with lower dimensional boundaries

Joseph Feneuil, Svitlana Mayboroda, Zihui Zhao

• Even in the context of the classical case d=n−1, (the analogues of) our results are new. The conditions on the coefficients are more relaxed than the previously known ones (most notably, we do not impose any restrictions whatsoever on the first n−1 rows of the matrix of coefficients) and the results are more general. We establish local rather than global estimates between the square function and the non-tangential maximal function and, perhaps even more importantly, we establish new Moser-type estimates at the boundary and improve the interior ones.