Teoremi di confronto di tipo Harnack per funzioni armoniche in domini con frontiera hölderiana
The Absolute Continuity of Elliptic Measure Revisited.
The boundary Harnack principle for the fractional Laplacian
We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.
Unbounded harmonic functions on homogeneous manifolds of negative curvature
We study unbounded harmonic functions for a second order differential operator on a homogeneous manifold of negative curvature which is a semidirect product of a nilpotent Lie group N and A = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(N). Then we single out a set of at most two of these coefficients which determine F. Then using asymptotic expansions we are able to prove some theorems...
Une Variante de L΄Epine De Lebesgue
Uniform domains and quasiconformal mappings on the Heisenberg groups.
Vertical variation of harmonic functions in upper half-spaces
Some results of Bourgain on the radial variation of harmonic functions in the disk are extended to the setting of harmonic functions in upper half-spaces.
Граничные свойства некоторых классов функций
О гармонических функциях классов
О граничных значениях решений эллиптических уравнений второго порядка
О модуле непрерывности гармонической функции в граничной точке
О собственных колебаниях трехмерного многослойного резонатора
Однозначная определенность областей с нежордановыми границами.
Отображения близких трехмерных областей и некоторые свойства метагармонических потенциалов