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Статья «FATOU-TYPE THEOREMS AND BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS IN THE UPPER HALF-SPACE, "Алгебра и анализ"»

Авторы:
  • MARTELL J. M.1
  • MITREA D.2
  • MITREA I.3
  • MITREA M.4
стр. 3-50
Платно
1 Instituto de Ciendas Matematicas, 2 University of Missouri Columbia, 3 Temple University, 4 University of Missouri Columbia
  • SDI: 007.001.0234-0852.2019.031.002.1
Ключевые слова:
  • Fatou-type theorem
  • Dirichlet boundary value problem
  • elliptic system
  • Poisson kernel
  • nontangential maximal operator
  • nontangential boundary trace
  • Muckenhoupt weights
  • Hardy space
  • bounded mean oscillations
  • vanishing mean oscillations
  • subcritical growth
  • sublinear growth
Аннотация:
This is a survey of recent progress in a program which to date has produced several publications and is aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space R for second-order, homogeneous, constant complex coefficient, elliptic systems L, formulated in a manner that emphasizes pointwise nontangential boundary traces of the null-solutions of L in R.

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