A Harnack inequality for fractional Laplace equations with lower order terms

By Jinggang Tan, Jingang Xiong. 2010

100 citations recorded by the source corpus.

We establish a Harnack inequality of fractional Laplace equations without imposing sign condition on the coefficient of zero order term via the Moser's iteration and John-Nirenberg inequality.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/527b1d33f2a4dd14d063412ab51e92744126830c

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In Applied Mathematics

Citations in the corpus

On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions (2011, methodology): “The following result is a refined version of that in [94].”
ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH THE FRACTIONAL LAPLACIAN (2013, background): “Recently, such type of estimates have been established in [23, 41, 42].”
Equations involving fractional Laplacian operator: Compactness and application (2015, methodology): “onents, though the methods used in [12, 13, 26] to obtain the estimates are diﬀerent from those in [14]. Problems with the fractional Laplacian have been extensively studied recently. See for example [3, 4, 6, 7, 8, 10, 11, 16, 20, 22, 23, 24]. In particular, the Br´ezis-Nirenberg type problem was d”
Nonlinear equations for fractional Laplacians I: Regularity, maximum principles, and Hamiltonian estimates (2010, unknown): “It has also been proved in [23] for the more general equation ∂νaφ + d(x)φ = b(x).”
On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, methodology): “Moreover, in this analysis, the regularity of the principal eigenfunction and a Harnack type inequality [16, 17, 61] for some non negative solution of (1.”