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

For 1 <  p  <  ∞ , we prove an  L   p  ‐version of the generalized Korn inequality for incompatible tensor fields  P  inW    0    1  ,    p    (  Curl  ;  Ω  ,    ℝ    3  ×  3    )  . More precisely, let   Ω  ⊂    ℝ    3be a bounded Lipschitz domain. Then there exists a constant  c  =  c ( p , Ω) > 0 such that‖  P    ‖L    p    (  Ω  ,    ℝ    3  ×  3    )    ≤  c‖  sym    P    ‖L    p    (  Ω  ,    ℝ    3  ×  3    )    +  ‖  Curl    P    ‖L    p    (  Ω  ,    ℝ    3  ×  3    )holds for all tensor fields   P  ∈    W    0    1  ,    p    (  Curl  ;  Ω  ,    ℝ    3  ×  3    )  , that is, for all   P  ∈    W    1  ,    p    (  Curl  ;  Ω  ,    ℝ    3  ×  3    )   with vanishing tangential trace   P  ×  ν  =  0   on  ∂ Ω where  ν  denotes the outward unit normal vector field to  ∂ Ω. For compatible   P  =  D  u  , this recovers an  L   p  ‐version of the classical Korn's first inequality and for skew‐symmetric   P  =  A   an  L   p  ‐version of the Poincaré inequality.

Nečas–Lions lemma revisited: An L p ‐version of the generalized Korn inequality for incompatible tensor fields