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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this class of domains. For some bounded domains › ‰ Rn presenting power type cusps of integer dimension mn¡2, we prove the existence of solutions of the equation divu = f in weighted Sobolev spaces, where the weights are powers of the distance to the cusp. The results obtained are optimal in the sense that the powers cannot be improved. As an application, we prove existence and uniqueness of solutions of the Stokes equations in appropriate spaces for cuspidal domains. Also, we obtain weighted Korn type inequalities for this class of domains. p 0(›), 1 < p < 1, where L p 0(›) denotes the space of functions in Lp(›) with vanishing mean value in ›. In other words, given any f 2 Lp0(›), there exists a solution u 2 W 1;p 0 (›) n of divu = f

Solutions of the divergence and Korn inequalities on domains with an external cusp