Symmetric solutions of the Neumann problem involving a critical Sobolev exponent

Jan Chabrowski, Pedro M. Girāo

DOI: http://dx.doi.org/10.12775/TMNA.2002.001

Abstract


We study the effect of the coefficient of the
critical nonlinearity for the Neumann problem
on existence of symmetric least energy solutions.
As a by-product we obtain two inequalities
in symmetric Sobolev spaces involving a weighted critical
Lebesgue norm and the $H^1$ norm.

Keywords


Neumann problem; critical Sobolev exponent; symmetric solutions; concentration-compactness principle; Sobolev inequalities

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