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Uniqueness and a
priori estimates for some nonlinear elliptic Neumann
equations in ℝ3
Juncheng Wei and Xingwang Xu |
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Vol. 221 (2005), No. 1, 159–165
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Abstract |
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Under some conditions on f(u), we show that for λ small and Ω ⊂ ℝ3 convex, the only solution to the elliptic equation Δu − λu + f(u) = 0 in Ω, with u > 0 in Ω and ∂u∕∂ν = 0 on ∂Ω, is constant. |
Keywords
critical Sobolev exponent, Neumann equation, nonlinear
elliptic PDEs
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Mathematical Subject Classification 2000
Primary: 35J60, 35B20
Secondary: 53C21
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Milestones
Received: 15 May 2001
Revised: 1 December 2001
Accepted: 5 December 2001
Published: 1 September 2005
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Authors |
| Juncheng Wei | |
| Department of Mathematics Chinese University of Hong Kong Shatin Hong Kong |
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| Xingwang Xu | |
| Department of Mathematics National University of Singapore Singapore 119260 Republic of Singapore |
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