scholarly journals Nonlinear elliptic equations on compact riemannian manifolds and asymptotics of Emden equations

1993 ◽  
Vol 112 (1) ◽  
pp. 445-445 ◽  
Author(s):  
Marie-Fran�oise Bidaut-Veron ◽  
Laurent Veron
2007 ◽  
Vol 18 (09) ◽  
pp. 1071-1111 ◽  
Author(s):  
JÉRÔME VÉTOIS

Let (M,g) be a smooth compact Riemannian n-manifold, n ≥ 4, and h be a Holdër continuous function on M. We prove multiplicity of changing sign solutions for equations like Δg u + hu = |u|2* - 2 u, where Δg is the Laplace–Beltrami operator and 2* = 2n/(n - 2) is critical from the Sobolev viewpoint.


1990 ◽  
Vol 114 (3-4) ◽  
pp. 213-227 ◽  
Author(s):  
Andrea Cianchi

SynopsisWe consider linear and nonlinear elliptic equations in divergence form on Riemannian manifolds with or without boundary. In the former case we impose a homogeneous Neumann boundary condition. By making use of isoperimetric inequalities for manifolds, we obtain a priori sharp estimates for the decreasing rearrangement of the solutions to such equations. These estimates enable us to derive bounds for suitable norms of the solutions and of their gradients.


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