Some remarks on elliptic problems with critical growth in the gradient

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Abstract

In this work we analyze existence, nonexistence, multiplicity and regularity of solution to problem { -Δu = β(u) ∇u 2 + λf(x) in Ω, {u = 0 on ∂Ω where β is a continuous nondecreasing positive function and f belongs to some suitable Lebesgue spaces. © 2005 Elsevier Inc. All rights reserved.

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Abdellaoui, B., Dall’Aglio, A., & Peral, I. (2006). Some remarks on elliptic problems with critical growth in the gradient. Journal of Differential Equations, 222(1), 21–62. https://doi.org/10.1016/j.jde.2005.02.009

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