Displaying similar documents to “Estimations of the best constant involving the L 2 norm in Wente’s inequality and compact H -surfaces in euclidean space”

On a fourth order equation in 3-D

Xingwang Xu, Paul C. Yang (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

On a model of rotating superfluids

Sylvia Serfaty (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider an energy-functional describing rotating superfluids at a rotating velocity ω , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω , and the derivation of a limiting free-boundary problem.

Estimations of the best constant involving the L norm in Wente's inequality and compact H-surfaces in Euclidean space

Ge Yuxin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In the first part of this paper, we study the best constant involving the L norm in Wente's inequality. We prove that this best constant is universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The second part concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to H-surfaces. We will establish the existence of a non-trivial critical point for a plan domain with small holes....