### Symmetric solutions of the Neumann problem involving a critical Sobolev exponent

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.

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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