Open AccessSparse recovery for inverse potential problems in divergence form
Author(s) -
Laurent Baratchart,
Cristobal Villalobos-Guillen,
Douglas P. Hardin,
Juliette Leblond,
Edward B. Saff
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1476/1/012009
Subject(s) - divergence (linguistics) , measure (data warehouse) , complement (music) , inverse , term (time) , set (abstract data type) , meaning (existential) , inverse problem , computer science , mathematics , zero (linguistics) , mathematical optimization , algorithm , combinatorics , data mining , mathematical analysis , physics , geometry , philosophy , linguistics , biochemistry , chemistry , quantum mechanics , complementation , gene , programming language , phenotype , psychology , psychotherapist
We discuss recent results from [10] on sparse recovery for inverse potential problem with source term in divergence form. The notion of sparsity which is set forth is measure- theoretic, namely pure 1-unrectifiability of the support. The theory applies when a superset of the support is known to be slender, meaning it has measure zero and all connected components of its complement has infinite measure in ℝ 3 . We also discuss open issues in the non-slender case.