A ‘sup + C inf’ inequality for the equation –Δu = V e<sup>u</sup>|x|<sup>2α</sup>
Bartolucci, Daniele; Bartolucci Daniele; University of Rome ‘Tor Vergata’
Журнал:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Дата:
2010
Аннотация:
We generalize the ‘sup+C inf’ inequality obtained by Shafrir to the solutions of$$ -\Delta u=\frac{V}{|x|^{2\alpha}}{\re^{u}}\quad\text{in }\varOmega, $$with Ω ⊂ ℝ<sup>2</sup> open and bounded, α ∈ (0,1) and V any measurable function which satisfies 0 < a ≤ V ≤ b < + ∞.
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