Harnack's inequality for some nonlocal equations and application

Jerome Coville

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Submission date: 11. Feb. 2008
Pages: 21
Bibtex
MSC-Numbers: 45A05, 47G10, 45M20, 47B34
Keywords and phrases: Integral operator, Hanarck's inequality, Positive solution
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Abstract:
In this paper, we establish a Harnack's inequality for positive solutions of the nonlocal inhomogeneous problem

where is an open set, J is a probability density with compact support and g,b are positive bounded functions. For some particular a(x), using the Harnack's Inequality, we also construct a positive solution of the above equation.