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Heat flow for the equation of surfaces with prescribed mean curvature.

Olivier Rey — 1991

Mathematische Annalen

Proof of two conjectures of H. Brezis and L.A. Peletier.

Olivier Rey — 1989

Manuscripta mathematica

Elliptic equations with limiting Sobolev exponent: the impact of the Green's function

Olivier Rey — 1992

Banach Center Publications

Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. Part II : $N \geq 4$

Olivier Rey; Juncheng Wei — 2005

Annales de l'I.H.P. Analyse non linéaire

Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity

Olivier Rey; Juncheng Wei — 2005

Journal of the European Mathematical Society

We show that the critical nonlinear elliptic Neumann problem $Δ u - μ u + u^{7 / 3} = 0$ in $Ω$ , $u > 0$ in $Ω$ , $\frac{\partial u}{\partial ν} = 0$ on $\partial Ω$ , where $Ω$ is a bounded and smooth domain in $ℝ^{5}$ , has arbitrarily many solutions, provided that $μ > 0$ is small enough. More precisely, for any positive integer $K$ , there exists $μ_{K} > 0$ such that for $0 < μ < μ_{K}$ , the above problem has a nontrivial solution which blows up at $K$ interior points in $Ω$ , as $μ \to 0$ . The location of the blow-up points is related to the domain geometry. The solutions are obtained as critical points of some finite-dimensional...

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Currently displaying 1 – 5 of 5

Heat flow for the equation of surfaces with prescribed mean curvature.

Proof of two conjectures of H. Brezis and L.A. Peletier.

Elliptic equations with limiting Sobolev exponent: the impact of the Green's function

Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. Part II : $N \geq 4$

Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity

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Formula preview

Currently displaying 1 – 5 of 5

Heat flow for the equation of surfaces with prescribed mean curvature.

Proof of two conjectures of H. Brezis and L.A. Peletier.

Elliptic equations with limiting Sobolev exponent: the impact of the Green's function

Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. Part II : N ≥ 4

Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity

Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. Part II : $N \geq 4$