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 Robin boundary value problem $\mathrm{div} (A \nabla u) =\mathrm{div} \mathbf{f}+F$ in $\Omega$, $\mathcal{C}^1$ domain, with $(A \nablau - \mathbf{f})\cdot \mathbf{n} + \alpha u = g$ on $\Gamma$, where the matrix$A$ belongs to $VMO (\mathbb{R}^3) $, and discover the uniform estimates on$\|u\|_{W^{1,p}(\Omega)}$, with $1 < p < \infty$, independent on $\alpha$. Atthe difference with the case $p = 2,$ which is simpler, we call here the weakreverse H\"older inequality. This estimates show that the solution of Robinproblem converges strongly to the solution of Dirichlet (resp. Neumann) problemin corresponding spaces when the parameter $\alpha$ tends to $\infty$ (resp.$0$).

Uniform $W^{1,p}$ estimate for elliptic operator with Robin boundary condition in $\mathcal{C}^1$ domain