Bounds on the Green function for integral operators and fractional harmonic measure with applications to boundary Harnack
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- by Luis A. Caffarelli and Yannick Sire PDF
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Abstract:
We prove a priori bounds on the Green function for general integral operators in divergence form in the spirit of Littman, Stampacchia and Weinberger’s result. For general linear integral operators with bounded measurable coefficients, we introduce the so-called fractional harmonic measure and prove several estimates on it. As an application, we prove a new boundary Harnack principle for these operators. Once the bounds on the Green function are known, the proof follows the approach of Caffarelli-Fabes-Mortola-Salsa and K. Bogdan.References
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Additional Information
- Luis A. Caffarelli
- Affiliation: Department of Mathematics, University of Texas at Austin, 2515 Speedway Stop C1200, Austin, Texas 78712
- MR Author ID: 44175
- Email: caffarel@math.utexas.edu
- Yannick Sire
- Affiliation: Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218
- MR Author ID: 734674
- Email: sire@math.jhu.edu
- Received by editor(s): April 26, 2017
- Received by editor(s) in revised form: May 4, 2017
- Published electronically: October 6, 2017
- Additional Notes: The first author was supported by NSF DMS-1540162
- Communicated by: Joachim Krieger
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1207-1216
- MSC (2010): Primary 35B45
- DOI: https://doi.org/10.1090/proc/13815
- MathSciNet review: 3750233