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

In this paper, we prove global-in-time $\dot{\mathrm{H}}^{\alpha,q}$-maximalregularity for a class of injective, but not invertible, sectorial operators ona UMD Banach space X , provided $q\in(1,+\infty) , $\alpha\in(-1+1/q,1/q)$. Wealso prove the corresponding trace estimate, so that the solution to thecanonical abstract Cauchy problem is continuous with values in a notnecessarily complete trace space.In order to put our result in perspective, wealso provide a short review on L q-maximal regularity which includes somerecent advances such as the revisited homogeneous operator and interpolationtheory by Danchin, Hieber, Mucha and Tolksdorf. This theory will be used tobuild the appropriate trace space, from which we want to choose the initialdata, and the solution of our abstract Cauchy problem to fall in.

Homogeneous Sobolev global-in-time maximal regularity and related trace estimates