English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the optimization problem of minimizing$\int_{\mathbb{R}^n}|\nabla u|^2\,\mathrm{d}x$ with double obstacles $\phi\lequ\leq\psi$ a.e. in $D$ and a constraint on the volume of$\{u>0\}\setminus\overline{D}$, where $D\subset\mathbb{R}^n$ is a boundeddomain. By studying a penalization problem that achieves the constrained volumefor small values of penalization parameter, we prove that every minimizer is$C^{1,1}$ locally in $D$ and Lipschitz continuous in $\mathbb{R}^n$ and thatthe free boundary $\partial\{u>0\}\setminus\overline{D}$ is smooth. Moreover,when the boundary of $D$ has a plane portion, we show that the minimizer is$C^{1,\frac{1}{2}}$ up to the plane portion.

An Optimization Problem in Heat Conduction With Volume Constraint and Double Obstacles