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math.AP2011★ 30 cited
Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials
Mousomi Bhakta, Roberta Musina
We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to second-order interpolation inequalities with weights.
math.FA2011
Caffarelli-Kohn-Nirenberg type inequalities for the weighted biharmonic operator: existence of extremal functions, breaking positivity and breaking symmetry
Paolo Caldiroli, Roberta Musina
We investigate Caffarelli-Kohn-Nirenberg type inequalities for the weighted biharmonic operator on cones, both under Navier and Dirichlet boundary conditions. Moreover, we study ex…
math.FA2011★ 4 cited
Rellich inequalities with weights
Paolo Caldiroli, Roberta Musina
Let be a cone in with . For every fixed we find the best constant in the Rellich inequality $\int_Ω|x|^α|Δu|^{2}dx\ge C\int_Ω|x|^{α-4}…