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Distributions for which div v = F has a continuous solution
Author(s) -
De Pauw Thierry,
Pfeffer Washek F.
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20204
Subject(s) - mathematics , bounded function , norm (philosophy) , sequence (biology) , open set , compact space , pure mathematics , set (abstract data type) , uniform continuity , combinatorics , discrete mathematics , mathematical analysis , metric space , biology , political science , computer science , law , genetics , programming language
The equation div v = F has a continuous weak solution in an open set U ⊂ ℝ m if and only if the distribution F satisfies the following condition: the F (φ i ) converge to 0 for every sequence {φ i } of test functions such that the support of each φ i is contained in a fixed compact subset of U , and in the L 1 norm, {φ i } converges to 0 and {∇φ i } is bounded. © 2007 Wiley Periodicals, Inc.