On the equivalence of Green functions for general Schrödinger operators on a half-space

Abdoul Ifra, and Lotfi Riahi. "On the equivalence of Green functions for general Schrödinger operators on a half-space." Annales Polonici Mathematici 83.1 (2004): 65-76. <http://eudml.org/doc/280911>.

@article{AbdoulIfra2004,
abstract = {We consider the general Schrödinger operator $L = div(A(x)∇_x) - μ$ on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function $G_\{Δ\}$ provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity $Kₙ^\{∞\}$ considered by Zhao and Pinchover. As an application we study the cone $_L(ℝⁿ₊)$ of all positive L-solutions continuously vanishing on the boundary xₙ = 0.},
author = {Abdoul Ifra, Lotfi Riahi},
journal = {Annales Polonici Mathematici},
keywords = {Green function; positive solution; Schrödinger operator},
language = {eng},
number = {1},
pages = {65-76},
title = {On the equivalence of Green functions for general Schrödinger operators on a half-space},
url = {http://eudml.org/doc/280911},
volume = {83},
year = {2004},
}

TY - JOUR
AU - Abdoul Ifra
AU - Lotfi Riahi
TI - On the equivalence of Green functions for general Schrödinger operators on a half-space
JO - Annales Polonici Mathematici
PY - 2004
VL - 83
IS - 1
SP - 65
EP - 76
AB - We consider the general Schrödinger operator $L = div(A(x)∇_x) - μ$ on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function $G_{Δ}$ provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity $Kₙ^{∞}$ considered by Zhao and Pinchover. As an application we study the cone $_L(ℝⁿ₊)$ of all positive L-solutions continuously vanishing on the boundary xₙ = 0.
LA - eng
KW - Green function; positive solution; Schrödinger operator
UR - http://eudml.org/doc/280911
ER -