کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4609545 | 1338517 | 2016 | 47 صفحه PDF | دانلود رایگان |
The goal of this paper is to study the effect of the Hardy potential on the existence and summability of solutions to a class of nonlocal elliptic problems{(−Δ)su−λu|x|2s=f(x,u) in Ω,u=0 in RN∖Ω,u>0 in Ω, where (−Δ)s(−Δ)s, s∈(0,1)s∈(0,1), is the fractional Laplacian operator, Ω⊂RNΩ⊂RN is a bounded domain with Lipschitz boundary such that 0∈Ω0∈Ω and N>2sN>2s. We will mainly consider the solvability in two cases:(1)The linear problem, that is, f(x,t)=f(x)f(x,t)=f(x), where according to the summability of the datum f and the parameter λ we give the summability of the solution u.(2)The problem with a nonlinear term f(x,t)=h(x)tσ for t>0t>0. In this case, existence and regularity will depend on the value of σ and on the summability of h.Looking for optimal results we will need a weak Harnack inequality for elliptic operators with singular coefficients that seems to be new.
Journal: Journal of Differential Equations - Volume 260, Issue 11, 5 June 2016, Pages 8160–8206