Sokołowski, Jan; Zolesio, Jean-Paul Shape sensitivity analysis of unilateral problems. (English) Zbl 0646.35036 SIAM J. Math. Anal. 18, 1416-1437 (1987). The authors give a general sensitivity analysis of abstract elliptic variational inequalities. The results are applied to unilateral problems, in particular, to the obstacle problem and to the Signorini problem in planar linear elasticity. The “shape derivatives” are characterized as the solutions of certain variational inequalities. Reviewer: J.Sprekels Cited in 2 ReviewsCited in 11 Documents MSC: 35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000) 49J40 Variational inequalities 49J52 Nonsmooth analysis 49K40 Sensitivity, stability, well-posedness Keywords:optimal shape design; sensitivity analysis; unilateral problems; obstacle problem; Signorini problem; planar linear elasticity; shape derivatives PDFBibTeX XMLCite \textit{J. Sokołowski} and \textit{J.-P. Zolesio}, SIAM J. Math. Anal. 18, 1416--1437 (1987; Zbl 0646.35036) Full Text: DOI