Properties of the extremal solution for a fourth-order elliptic problem
2012 ◽
Vol 142
(5)
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pp. 1051-1069
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Keyword(s):
Let λ* > 0 denote the largest possible value of λ such that the systemhas a solution, where $\mathbb{B}$ is the unit ball in ℝn centred at the origin, p > 1 and n is the exterior unit normal vector. We show that for λ = λ* this problem possesses a unique weak solution u*, called the extremal solution. We prove that u* is singular when n ≥ 13 for p large enough and actually solve part of the open problem which Dávila et al. left unsolved.
2011 ◽
Vol 30
(1)
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pp. 227-241
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Keyword(s):
2014 ◽
Vol 420
(1)
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pp. 532-550
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Keyword(s):
2010 ◽
Vol 248
(3)
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pp. 594-616
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1982 ◽
Vol 26
(3-4)
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pp. 357-361
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Keyword(s):
2016 ◽
Vol 146
(1)
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pp. 195-212
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2006 ◽
Vol 230
(2)
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pp. 743-770
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Keyword(s):