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Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions

Abstract : In this note we present some uniqueness and comparison results for a class of problem of the form (0.1) −Lu = H(x, u, ∇u) + h(x), u ∈ H1 0 (Ω) ∩ L∞(Ω), where Ω ⊂ R N , N ≥ 2 is a bounded domain, L is a general elliptic second order linear operator with bounded coefficients and H is allowed to have a critical growth in the gradient. In some cases our assumptions prove to be sharp.
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Submitted on : Monday, July 4, 2022 - 5:09:34 PM
Last modification on : Wednesday, July 13, 2022 - 3:53:16 AM

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David Arcoya, Colette De Coster, Louis Jeanjean, Kazunaga Tanaka. Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions. Journal of Mathematical Analysis and Applications, Elsevier, 2014, 420 (1), pp.772-780. ⟨10.1016/j.jmaa.2014.06.007⟩. ⟨hal-03138844⟩

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