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

• Autorzy: Abdoul Ifra , Lotfi Riahi
• Języki publikacji: EN

Abstrakty

EN

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 $𝓒_L(ℝⁿ₊)$ of all positive L-solutions continuously vanishing on the boundary {xₙ = 0}.

Kategorie tematyczne

• 31B25: Boundary behavior
• 31B05: Harmonic, subharmonic, superharmonic functions
• 35J60: Nonlinear elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 83
• Numer: 1
• Strony: 65-76

Daty

wydano

2004

Twórcy

autor

Abdoul Ifra

• Department of Mathematics, Faculty of Sciences of Tunis, Campus Universitaire, 1060 Tunis, Tunisia

autor

Lotfi Riahi

• Department of Mathematics, Faculty of Sciences of Tunis, Campus Universitaire, 1060 Tunis, Tunisia

Identyfikatory

DOI

10.4064/ap83-1-8