Details

Autor(en) / Beteiligte

• Raiță, Bogdan
• Skorobogatova, Anna

Titel

Continuity and canceling operators of order n on Rn

Ist Teil von

• Calculus of variations and partial differential equations, 2020, Vol.59 (2)

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We prove that for elliptic and canceling linear partial differential operators B of order n on R n , continuity of a map u can be inferred from the fact that B u is a measure. We also prove strict continuity of the embedding of the space BV B ( R n ) into the space of continuous functions vanishing at infinity. Here, BV B ( Ω ) denotes the space of vector fields u ∈ W n - 1 , 1 ( Ω ) such that B u is a finite vectorial measure on the open set Ω ⊂ R n . For cubes Q ⊂ R n , the class of operators B such that BV B ( Q ) ⊂ C ( Q ¯ ) is also characterized.