Nonlinear elliptic problem related to the Hardy inequality with singular term at the boundary
2015 ◽
Vol 17
(03)
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pp. 1450033
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Keyword(s):
Let Ω ⊂ ℝNbe a bounded regular domain of ℝNand 1 < p < ∞. The paper is divided into two main parts. In the first part, we prove the following improved Hardy inequality for convex domains. Namely, for all [Formula: see text], we have [Formula: see text] where d(x) = dist (x, ∂Ω), [Formula: see text] and C is a positive constant depending only on p, N and Ω. The optimality of the exponent of the logarithmic term is also proved. In the second part, we consider the following class of elliptic problem [Formula: see text] where 0 < q ≤ 2* - 1. We investigate the question of existence and nonexistence of positive solutions depending on the range of the exponent q.
2021 ◽
Vol 1931
(1)
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pp. 012002
Keyword(s):
2010 ◽
Vol 2010
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pp. 1-11
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2019 ◽
Vol 266
(8)
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pp. 4835-4863
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Keyword(s):
2012 ◽
Vol 18
(4)
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pp. 941-953
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Keyword(s):
2016 ◽
Vol 435
(2)
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pp. 1710-1737
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2010 ◽
Vol 368
(2)
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pp. 400-412
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2006 ◽
Vol 23
(1)
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pp. 220-233
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