The Dirichlet problem in domains with lower dimensional boundaries

• Joseph Feneuil ^[1] ; Svitlana Mayboroda ^[2] ; Zihui Zhao ^[3]
  1. [1] Temple University

     Temple University

     City of Philadelphia, Estados Unidos

     
  2. [2] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
  3. [3] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 3, 2021, págs. 821-910
• Idioma: inglés
• DOI: 10.4171/rmi/1208
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.