2020
DOI: 10.1007/s00028-020-00623-9
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Existence and nonexistence of positive solutions to a fractional parabolic problem with singular weight at the boundary

Abstract: In this work, we consider a nonlocal semilinear parabolic problem related to a fractional Hardy inequality with singular weight at the boundary. More precisely, we consider the problem (P)      ut + (−∆) s u = λ u p d 2s in Ω T = Ω × (0, T), u(x, 0) = u 0 (x) in Ω, u = 0 in (IR N \ Ω) × (0, T), where 0 < s < 1, Ω ⊂ IR N is a bounded regular domain, d(x) = d(x, ∂Ω), p > 0 and λ > 0 is a positive constant. The initial data u 0 0 is a nonnegative function in a suitable Lebesgue space that we make precise lat… Show more

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Cited by 4 publications
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“…Restricted fractional Laplacian (FL Rest ). In this subsection, we will introduce another fractional Laplacian operator called restricted fractional Laplacian, 3 which we denote (−∆) s Rest . It is defined for any u ∈ X s 0 (Ω) by the formula…”
mentioning
confidence: 99%
“…Restricted fractional Laplacian (FL Rest ). In this subsection, we will introduce another fractional Laplacian operator called restricted fractional Laplacian, 3 which we denote (−∆) s Rest . It is defined for any u ∈ X s 0 (Ω) by the formula…”
mentioning
confidence: 99%