We prove existence of extremal functions for some Rellich-Sobolev type inequalities involving the L2 norm of the Laplacian as a leading term and the L2 norm of the gradient, weighted with a Hardy potential. Moreover we exhibit a symmetry breaking phenomenon when the nonlinearity has a growth close to the critical one and the singular potential increases in strength.
Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on Rn
CALDIROLI, Paolo
2014-01-01
Abstract
We prove existence of extremal functions for some Rellich-Sobolev type inequalities involving the L2 norm of the Laplacian as a leading term and the L2 norm of the gradient, weighted with a Hardy potential. Moreover we exhibit a symmetry breaking phenomenon when the nonlinearity has a growth close to the critical one and the singular potential increases in strength.
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