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 :
Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity
We show that the critical nonlinear elliptic Neumann problem in , in , on , where is a bounded and smooth domain in , has arbitrarily many solutions, provided that is small enough. More precisely, for any positive integer , there exists such that for , the above problem has a nontrivial solution which blows up at interior points in , as . 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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