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

That the weak solutions of degenerate parabolic pdes modelled on theinhomogeneous $p-$Laplace equation $$ u_t - \mathrm{div} \left(|\nabla u|^{p-2}\nabla u \right) = f \in L^{q,r}, \quad p>2 $$ are $C^{0,\alpha}$, for some$\alpha \in (0,1)$, is known for almost 30 years. What was hitherto missingfrom the literature was a precise and sharp knowledge of the H\"older exponent$\alpha$ in terms of $p, q, r$ and the space dimension $n$. We show in thispaper that $$ \alpha = \frac{(pq-n)r-pq}{q[(p-1)r-(p-2)]}, $$ using a methodbased on the notion of geometric tangential equations and the intrinsic scalingof the $p-$parabolic operator. The proofs are flexible enough to be of use in anumber of other nonlinear evolution problems.

A geometric tangential approach to sharp regularity for degenerate evolution equations