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Extremal Functions for a Mean Field Equation in Two Dimension
Extremal Functions a Mean Field Equation Two Dimension
2014/4/3
Let be a bounded piecewise C 2 simply-connected domain. In thisarticle, we give necessary and sucient conditions for the existence ofmaximizer ofJ8() = log Zedx!116Zj 5 j2dx for 2 H10(). We pro...
Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants
Caffarelli-Kohn-Nirenberg inequality Gagliardo-Nirenberg inequality loga-rithmic Hardy inequality logarithmic Sobolev inequality
2010/12/14
This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WL...