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 characterize the existence of solutions to the quasilinear Riccati typeequation \begin{eqnarray*} \left\{ \begin{array}{rcl} -{\rmdiv}\,\mathcal{A}(x, \nabla u)&=& |\nabla u|^q + \sigma \quad \text{in}~\Omega, \\ u&=&0 \quad \text{on}~ \partial \Omega, \end{array}\right.\end{eqnarray*} with a distributional or measure datum $\sigma$. Here ${\rmdiv}\,\mathcal{A}(x, \nabla u)$ is a quasilinear elliptic operator modeledafter the $p$-Laplacian ($p>1$), and $\Omega$ is a bounded domain whoseboundary is sufficiently flat (in the sense of Reifenberg). For distributionaldata, we assume that $p>1$ and $q>p$. For measure data, we assume that they arecompactly supported in $\Omega$, $p>\frac{3n-2}{2n-1}$, and $q$ is in thesub-linear range $p-1<q<1$. We also assume more regularity conditions on$\mathcal{A}$ and on $\partial\Omega$ in this case.

Quasilinear Riccati type equations with oscillatory and singular data