@Article{JMS-53-402,
author = {Case , Jeffrey S. and Wang , Yi},
title = {Towards a Fully Nonlinear Sharp Sobolev Trace Inequality},
journal = {Journal of Mathematical Study},
year = {2020},
volume = {53},
number = {4},
pages = {402--435},
abstract = {<p style="text-align: justify;">We classify local minimizers of $\int\sigma_2+\oint H_2$ among all conformally flat metrics in the Euclidean $(n+1)$-ball, $n=4$ or $n=5$, for which the boundary has unit volume, subject to an ellipticity assumption. We also classify local minimizers of the analogous functional in the critical dimension $n+1=4$. If minimizers exist, this implies a fully nonlinear sharp Sobolev trace inequality. Our proof is an adaptation of the Frank-Lieb proof of the sharp Sobolev inequality, and in particular does not rely on symmetrization or Obata-type arguments.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v53n4.20.02},
url = {http://global-sci.org/intro/article_detail/jms/18508.html}
}