Artículos de revistas
Optimization problem for extremals of the trace inequality in domains with holes
del Pezzo, Leandro Martin; Optimization problem for extremals of the trace inequality in domains with holes; World Scientific; Communications In Contemporary Mathematics; 12; 4; 8-2010; 569-586
del Pezzo, Leandro Martin
We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this formula, we prove that when Ω is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case.