Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $R^n$
Paolo Caldiroli
Communications on Pure & Applied Analysis 2014, 13(2): 811-821 doi: 10.3934/cpaa.2014.13.811
We prove existence of extremal functions for some Rellich-Sobolev type inequalities involving the $L^2$ norm of the Laplacian as a leading term and the $L^2$ norm of the gradient, weighted with a Hardy potential. Moreover we exhibit a breaking symmetry phenomenon when the nonlinearity has a growth close to the critical one and the singular potential increases in strength.
keywords: breaking symmetry. extremal functions Rellich-Sobolev inequality Biharmonic operator

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