EUDML

Let $Δ u = Σ_{i} \frac{\partial^{2}}{\partial_{x_{i}}^{2}}$ , $L u = Σ_{i, j} a_{i j} \frac{\partial^{2}}{\partial x_{i} \partial x_{j}} u + Σ_{i} b_{i} \frac{\partial}{\partial x_{i}} u + c u$ be elliptic operators with Hölder continuous coefficients on a bounded domain $Ω \subset R^{n}$ of class $C^{1, 1}$ . There is a constant $c > 0$ depending only on the Hölder norms of the coefficients of $L$ and its constant of ellipticity such that $c^{- 1} G_{Δ}^{Ω} \leq G_{L}^{Ω} \leq c G_{Δ}^{Ω} on Ω \times Ω,$ where $γ_{Δ}^{Ω}$ (resp. $G_{L}^{Ω}$ ) are the Green functions of $Δ$ (resp. $L$ ) on $Ω$ .

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The Dirichlet problem for sublaplacians on nilpotent Lie groups - geometric criteria for regularity

Wiener's Criterion in Potential Theory with Applications to Nilpotent Lie Groups.

On boundary Harnack principles and poles of extremal harmonic functions.

The Dirichlet Problem for Sublaplacians on Nilpotent Gruops - Geometric Criteria For Regularity.

Asymptotics for some Green Kernels on the Heisenberg Group and the Martin Boundary.

Uniform bounds for quotients of Green functions on $C^{1, 1}$ -domains