Optimization problem for extremals of the trace inequality in domains with holes
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 criti...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02191997_v12_n4_p569_DelPezzo |
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| Sumario: | 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. © 2010 World Scientific Publishing Company. |
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