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- W2022285166 abstract "In this paper, we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non-linearity and combine these results with the localization method introduced in [López-Gómez, The boundary blow-up rate of large solutions, J. Differential Equations 195 (2003) 25–45] to prove that any large solution L of Δ u = a ( x ) u p , p > 1 , a > 0 , must satisfy lim x → x 0 L ( x ) F x 0 ( dist ( x , ∂ Ω ) ) = I 0 - p p - 1 p + 1 p - 1 p + 1 p - 1 for each x 0 ∈ ∂ Ω , where F x 0 ( t ) := ∫ t ∞ ∫ 0 s f x 0 1 p + 1 - p + 1 p - 1 ds , I 0 := lim t ↓ 0 F x 0 ( t ) F x 0 ′ ′ ( t ) [ F x 0 ′ ( t ) ] 2 and f x 0 is any smooth extension of the boundary normal section of a at x 0 ∈ ∂ Ω , i.e., f x 0 ( t ) = a ( x 0 - t n x 0 ) , t > 0 , t ∼ 0 . Subsequently, n x 0 stands for the outward unit normal at x 0 ∈ ∂ Ω . Therefore, the theory can be extended to cover the general case when f x 0 ∈ L 1 p + 1 ." @default.
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- W2022285166 date "2006-05-01" @default.
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- W2022285166 title "Optimal uniqueness theorems and exact blow-up rates of large solutions" @default.
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- W2022285166 doi "https://doi.org/10.1016/j.jde.2005.08.008" @default.
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