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 prove the local H\"older regularity of weak solutions to the mixed localnonlocal parabolic equation of the form \begin{equation*} u_t-\Deltau+\text{P.V.}\int_{\mathbb{R}^{n}}{\frac{u(x,t)-u(y,t)}{{\left|x-y\right|}^{n+2s}}}dy=0, \end{equation*} where$0<s<1$; for every exponent $\alpha_0\in(0,1)$. Here, $\Delta$ is the usualLaplace operator. Next, we show that the gradients of weak solutions are also$\alpha$-H\"older continuous for some $\alpha\in (0,1)$. Our approach is purelyanalytic and it is based on perturbation techniques.

Gradient H\"older regularity in mixed local and nonlocal linear parabolic problem