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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the mixed local and nonlocal double phase parabolic equation\begin{align*} \partial_t u(x,t)-\mathrm{div}(a(x,t)|\nabla u|^{q-2}\nabla u)+\mathcal{L}u(x,t)=0 \end{align*} in $Q_T=\Omega\times(0,T)$, where$\mathcal{L}$ is the nonlocal $p$-Laplace type operator. The local boundednessof weak solutions is proved by means of the De Giorgi-Nash-Moser iteration withthe nonnegative coefficient function $a(x,t)$ being bounded. In addition, when$a(x,t)$ is H\"{o}lder continuous, we discuss the pointwise behavior and lowersemicontinuity of weak supersolutions based on energy estimates and De Giorgitype lemma. Analogously, the corresponding results are also valid for weaksubsolutions.

Regularity of weak solutions for mixed local and nonlocal double phase parabolic equations