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Strong maximum principles for fractional Laplacians

Part of: Miscellaneous topics - Partial differential equations Partial differential equations

Published online by Cambridge University Press:  16 January 2019

Roberta Musina  and
Alexander I. Nazarov
Roberta Musina
Affiliation:
Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, via delle Scienze, 206 – 33100, Udine, Italy (roberta.musina@uniud.it)
Alexander I. Nazarov
Affiliation:
St. Petersburg Department of Steklov Institute, Fontanka 27, St. Petersburg 191023, Russia and St. Petersburg State University, Universitetskii pr. 28, St. Petersburg 198504, Russia (al.il.nazarov@gmail.com)
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Abstract

We give a unified approach to strong maximum principles for a large class of nonlocal operators of order s ∈ (0, 1) that includes the Dirichlet, the Neumann Restricted (or Regional) and the Neumann Semirestricted Laplacians.

Keywords

Fractional Laplace operatorsmaximum principle

MSC classification

Primary: 35R11: Fractional partial differential equations
Secondary: 35B50: Maximum principles
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 5 , October 2019 , pp. 1223 - 1240
Copyright
Copyright © Royal Society of Edinburgh 2019 

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