Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian

V. Gol'dshtein, V. Pchelintsev, A. Ukhlov

Результат исследования: Материалы для журналаСтатья


In this paper we study integral estimates of derivatives of conformal mappings φ:D→Ω of the unit disc D⊂C onto bounded domains Ω that satisfy the Ahlfors condition. These integral estimates lead to estimates of constants in Sobolev–Poincaré inequalities, and by the Rayleigh quotient we obtain spectral estimates of the Neumann–Laplace operator in non-Lipschitz domains (quasidiscs) in terms of the (quasi)conformal geometry of the domains. Specifically, the lower estimates of the first non-trivial eigenvalues of the Neumann–Laplace operator in some fractal type domains (snowflakes) were obtained.

Язык оригиналаАнглийский
Страницы (с... по...)19-39
Количество страниц21
ЖурналJournal of Mathematical Analysis and Applications
Номер выпуска1
Статус публикацииОпубликовано - 1 июл 2018


ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics