Characterization of concentration points and L - estimates for solutions of a Semilinear Neumann problem involving the critical Sobolev exponent

Adimurthi, ; Pacella, Filomena ; Yadava, S. L. (1995) Characterization of concentration points and L - estimates for solutions of a Semilinear Neumann problem involving the critical Sobolev exponent Differential and Integral Equations, 8 (1). pp. 41-68. ISSN 0893-4983

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Abstract

Let Ω ⊂ Rn(n ≥ 7) be a bounded domain with smooth boundary. For λ > 0, let uλ be a solution of -Δu + λu= un+2/n-2 in Ω. u > 0 in Ω, ∂u/∂v = 0 on ∂Ω, whose energy is less than the first critical level. Here we study the blow up points and the L - estimates of uλ as λ → ∞. We show that the blow up points are critical points of the mean curvature on the boundary.

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Deposited On:30 Jun 2012 08:08
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