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We investigate Caffarelli-Kohn-Nirenberg type inequalities for the weightedbiharmonic operator on cones, both under Navier and Dirichlet boundaryconditions. Moreover, we study existence and qualitative properties of extremalfunctions. In particular, we show that in some cases extremal functions dochange sign; when the domain is the whole space, we prove some breakingsymmetry phenomena.

Caffarelli-Kohn-Nirenberg type inequalities for the weighted biharmonic  operator: existence of extremal functions, breaking positivity and breaking  symmetry