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

The objects to be studied are the null-spaces of linear first-order elliptic partial differential operators with domain      H 1 ( R n ; C k ) {H_1}({R^n};{C^k})       in      L 2 ( R n ; C k ) {L_2}({R^n};{C^k})      , the first-order coefficients of which become constant and the zero-order coefficients of which vanish outside a compact set in      R n {R^n}      . An example is given of an operator of this type which has a nontrivial null-space. It is shown that the dimension of the null-space of such an operator is finite for any number  n  of independent variables, and that this dimension is an upper-semicontinuous function of the operator in a certain sense.

On the null-spaces of first-order elliptic partial differential operators in 𝑅ⁿ