Divergence L 2-Coercivity Inequalities

Giles Auchmuty
2006 Numerical Functional Analysis and Optimization  
This paper describes sharp L 2 −coercivity inequalities for the divergence operator on bounded Lipschitz regions in R n . The inequalities are given in a manner which scales under dilations of the region. The optimal constants in the inequality are identified as the least eigenvalue of a biharmonic problem or else of a non-standard problem for the Dirichlet Laplacian. When n = 2, a coercivity result for the curl operator is also obtained. DIVERGENCE L 2 − COERCIVITY. 9
doi:10.1080/01630560600790777 fatcat:mzmaqxazm5grphuyor5nuucxee