Potential theory for the Schrödinger equation

DOI10.1090/S0273-0979-1986-15478-9zbMath0613.60068MaRDI QIDQ4720497

Eugene B. Fabes, Michael Craig Cranston, Zhongxin Zhao

Publication date: 1986

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationHarnack's inequalityharmonic measuresuniformly elliptic operator

Mathematics Subject Classification ID

Probabilistic potential theory (60J45) Boundary behavior of harmonic functions in higher dimensions (31B25)

Related Items (9)

On an estimate of Cranston and McConnell for elliptic diffusions in uniform domains ⋮ On the lift-off constant for elastically supported plates ⋮ Conditional transformation of drift formula and potential theory for \(\Delta +b(\cdot)\cdot \nabla\) ⋮ On the lifetime of a conditioned Brownian motion in the ball ⋮ Hölder-continuity of solutions for some Schrödinger equations ⋮ The probabilistic solution of the Dirichlet problem for \({1\over2}\Delta+\langle a,\nabla\rangle+b\) with singular coefficients ⋮ Among all two-dimensional convex domains the disk is not optimal for the lifetime of a conditioned Brownian motion ⋮ On a conditioned Brownian motion and a maximum principle on the disk ⋮ Green's functions for the Schrödinger equation with short-range potentials

Cites Work

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• Uniform boundedness of conditional gauge and Schrödinger equations
• Necessary and sufficient conditions for absolute continuity of elliptic- harmonic measure
• Le problème de Dirichlet pour l'opérateur de Schrödinger
• Green function for Schrödinger operator and conditioned Feynman-Kac gauge
• Conditional Brownian motion in rapidly exhaustible domains
• Harnack's Inequality for Schrodinger Operators and the Continuity of Solutions
• Conditional brownian motion and the boundary limits of harmonic functions
• Conditional gauge with unbounded potential
• Lifetime of conditioned Brownian motion in Lipschitz domains
• On the Absolute Continuity of Elliptic Measures
• Brownian motion and harnack inequality for Schrödinger operators

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