Optimization problem for extremals of the trace inequality in domains with holes
Analysis of PDEs
2013-11-15 v1
Abstract
We study the Sobolev trace constant for functions defined in a bounded domain that vanish in the subset 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 is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case.
Cite
@article{arxiv.0809.0246,
title = {Optimization problem for extremals of the trace inequality in domains with holes},
author = {L. M. Del Pezzo},
journal= {arXiv preprint arXiv:0809.0246},
year = {2013}
}
Comments
13 pages