4 citations · 4 across the 5 of their papers we have counts for
5 papers
Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on
Paolo Caldiroli
We prove existence of extremal functions for some Rellich-Sobolev type inequalities involving the norm of the Laplacian as a leading term and the norm of the gradie…
A class of second order dilation invariant inequalities
Paolo Caldiroli, Roberta Musina
We compute the best constants in some second order dilation invariant inequalities, with weights being powers of the distance from the origin.
Radial graphs over domains of with prescribed mean curvature
Paolo Caldiroli, Giovanni Gullino
We prove the existence and uniqueness of radial graphs over a given domain of having boundary on the sphere and whose mean curvature at every poin…
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…
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}…