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math.OC2023
Shape of extremal functions for weighted Sobolev-type inequalities
Friedemann Brock, Francesco Chiacchio, Gisella Croce +1
We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions…
math.AP2023
Isoperimetric sets for weighted twisted eigenvalues
Barbara Brandolini, Antoine Henrot, Anna Mercaldo +1
In tis paper we prove an isoperimetric inequality for the first twisted eigenvalue of a weighted operator, defined as the minimum of the usual Rayleigh quotient when…