caa a22 4500 469085061 CHVBK 20180323133002.0 cr unu---uuuuu 170328e19920201xx s 000 0 eng 10.1007/BF00041649 doi (NATIONALLICENCE)springer-10.1007/BF00041649 Ramaswamy Mythily Tata Institute of Fundamental Research Centre, P.O. Box 1234, 560 012, Bangalore, India aut On a counterexample to a conjecture of Saint Venant [Elektronische Daten] [Mythily Ramaswamy] The elliptic boundary value problem % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqGHsi% slcqGHuoarcaWG1bGaeyypa0dccaGae8hiaaIaaGymaiab-bcaGiab% -bcaGiab-bcaGiaabMgacaqGUbGaaeiiaiabfM6axjaabYcaaeaaae% aacaWG1bGaeyypa0JaaGimaiab-bcaGiab-bcaGiab-bcaGiaab+ga% caqGUbGaaeiiaiabgkGi2kabfM6axjaabYcaaaaa!4E11!\[\begin{gathered}- \Delta u = 1 {\text{in }}\Omega {\text{,}} \hfill \\\hfill \\u = 0 {\text{on }}\partial \Omega {\text{,}} \hfill \\\end{gathered}\]is considered. The Saint Venant's conjecture for convex plane domains Ω, having symmetry about two orthogonal axes, is that the maximum of |∇u| occurs only at the points on ∂Ω which are nearest to the origin. G. Sweers constructed one such domain Ω and claimed that either the conjecture fails for Ω or for Ωε={(x, y)∈Ω;u(x, y) >ε}, which again is convex. We give a totally different proof of this claim. Our proof brings out clearly the reason for the failure of the conjecture and also allows us to construct many more such domains. Kluwer Academic Publishers, 1992 Journal of Elasticity Kluwer Academic Publishers 27/2(1992-02-01), 183-192 0374-3535 27:2<183 1992 27 10659 https://doi.org/10.1007/BF00041649 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00041649 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ramaswamy Mythily Tata Institute of Fundamental Research Centre, P.O. Box 1234, 560 012, Bangalore, India aut NATIONALLICENCE 773 0- Journal of Elasticity Kluwer Academic Publishers 27/2(1992-02-01), 183-192 0374-3535 27:2<183 1992 27 10659 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer