Abstract
Let [Formula: see text], [Formula: see text] be a bounded open domain in [Formula: see text] ([Formula: see text]) with a [Formula: see text] boundary [Formula: see text] and [Formula: see text] be a Hausdorff measure on [Formula: see text]. We denote by [Formula: see text] [Formula: see text] where [Formula: see text] is the unit inward normal vector of [Formula: see text] at point [Formula: see text] and [Formula: see text] Our purpose of this paper is to study a nonlocal elliptic problem involving gradient nonlinearity [Formula: see text] where [Formula: see text], the operator [Formula: see text] is the fractional Laplacian and [Formula: see text] is a locally Hölder continuous function satisfying some extra condition. We show that the above problem admits a nonnegative weak solution [Formula: see text], which is a classical solution of [Formula: see text]
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