1 results
A uniqueness result for a singular elliptic equation with gradient term
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 5 / October 2018
- Published online by Cambridge University Press:
- 22 June 2018, pp. 983-994
- Print publication:
- October 2018
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- Article
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We prove the uniqueness of a solution for a problem whose simplest model is
with k ≥ 1, 0
f ∈ L∞(Ω) and Ω is a bounded domain of ℝN, N ≥ 2. So far, uniqueness results are known for k < 1, while existence holds for any k ≥ 1 and f positive in open sets compactly embedded in a neighbourhood of the boundary. We extend the uniqueness results to the k ≥ 1 case and show, with an example, that existence does not hold if f is zero near the boundary. We even deal with the uniqueness result when f is replaced by a nonlinear term λuq with 0 < q < 1 and λ > 0.
