# Hierarchical Construction of Bounded Solutions in Critical Regularity Spaces

@article{Tadmor2010HierarchicalCO,
title={Hierarchical Construction of Bounded Solutions in Critical Regularity Spaces},
journal={Communications on Pure and Applied Mathematics},
year={2010},
volume={69}
}
• Published 7 March 2010
• Mathematics
• Communications on Pure and Applied Mathematics
We construct uniformly bounded solutions for the equations div U = f and U = f in the critical cases f∈L#d(Td,ℝ) and f∈L#3(T3,ℝ3) , respectively. Criticality in this context manifests itself by the lack of a linear solution operator mapping L#d↦ L∞(Td) . Thus, the intriguing aspect here is that although the problems are linear, construction of their solutions is not. Our constructions are special cases of a general framework for solving linear equations of the form LU=f , where L is a linear…
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