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arXiv · 0809.0246

Optimization problem for extremals of the trace inequality in domains with holes

L. M. Del Pezzo
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Abstract

We study the Sobolev trace constant for functions defined in a bounded domain $Ø$ that vanish in the subset $A.$ We find a formula for the first variation of the Sobolev trace with respect to hole. As a consequence of this formula, we prove that when $Ø$ is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case.

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L. M. Del Pezzo. 2008-09-01. Optimization problem for extremals of the trace inequality in domains with holes. https://doi.org/10.1142/s0219199710003920

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