Maximal solutions of semilinear elliptic equations with locally integrable forcing term |
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Authors: | Moshe Marcus Laurent Véron |
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Institution: | (1) Department of Mathematics, Technion - Israel Institute of Technology, 32000 Haifa, Israel;(2) Laboratoire de Mathématiques, Faculté des Sciences, Parc de Grandmont, 37200 Tours, France |
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Abstract: | We study the existence of a maximal solution of −Δu+g(u)=f(x) in a domain Ω ∈ ℝ
N
with compact boundary, assuming thatf ∈ (L
loc
1
(Ω))+ and thatg is nondecreasing,g(0)≥0 andg satisfies the Keller-Osserman condition. We show that if the boundary satisfies the classicalC
1,2 Wiener criterion, then the maximal solution is a large solution, i.e., it blows up everywhere on the boundary. In addition,
we discuss the question of uniqueness of large solutions.
This research was partially supported by an EC Grant through the RTN Program “Front-Singularities”, HPRN-CT-2002-00274. |
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Keywords: | |
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