On the shape of solutions to some variational problems
Kawohl, Bernd
Nonlinear Analysis, Function Spaces and Applications, GDML_Books, (1994), p. 77-102 / Harvested from
EUDML-ID : urn:eudml:doc:220821
Mots clés:
@article{702460,
     title = {On the shape of solutions to some variational problems},
     booktitle = {Nonlinear Analysis, Function Spaces and Applications},
     series = {GDML\_Books},
     publisher = {Prometheus Publishing House},
     address = {Praha},
     year = {1994},
     pages = {77-102},
     mrnumber = {MR1322310},
     zbl = {0841.49022},
     url = {http://dml.mathdoc.fr/item/702460}
}
Kawohl, Bernd. On the shape of solutions to some variational problems, dans Nonlinear Analysis, Function Spaces and Applications, GDML_Books,  (1994), pp. 77-102. http://gdmltest.u-ga.fr/item/702460/

Buttazzo, G.; Ferone, V.; Kawohl, B. Minimum problems over sets of concave functions and related questions, Preprint 93–55, Institut für Wissenschaftliches Rechnen und SFB 359, Heidelberg, submitted to Math. Nachr.. | MR 1336954 | Zbl 0835.49001

Kawohl, B.; Schwab, C. Convergent finite elements for a class of nonconvex variational problems, Preprint 94–10, Institut für Wissenschaftliches Rechnen und SFB 359, Heidelberg, submitted to Numer. Math.. | MR 1492052 | Zbl 0908.65052

Newton, I. Philisophiae Naturalis Principia Mathematica, 1686. (1686)

Saint Venant, B. de Mémoire sur la torsion des prismes, avec des considérations sur leur flexion ainsi que sur l’équilibre intérieur des solides élastiques en général, et de formules pratiques pour le calcul de leur résistance á divers efforts s’exercant simultanément, Mémoires présentés par divers savants á l’Académie des sciences de l’institut impérial de France, 2 Sér. 14 (1856), 233–560. (1856)

Thomson, W.; Tait, P.G. Treatise on natural philosophy, 1st edn., Oxford, 1867. (1867)

Boussinesq, J. Étude nouvelle sur l’equilibre et le movement des corp solides élastiques dont certaines dimensions sont très-petit per rapport à d’autres, J. Math. Pures Appl. 16 (1871), 125–274. (1871)

Filon, L.N.G. On the resistance to torsion of certain forms of shafting, with special reference to the effect of keyways, Philos. Trans. Roy. Soc. London Ser. A 193 (1900), 309–352. (1900)

Polya, G. Liegt die Stelle der größten Beanspruchung an der Oberfläche?, Z. Angew. Math. Mech. 10 (1930), 353–360. (1930)

Polya, G.; Szegö, G. Isoperimetric Inequalities in Mathematical Physics, Ann. of Math. Stud. 27 (1951), Princeton Univ. Press. (1951) | MR 0043486

Serrin, J. The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Phil. Trans. Roy. Soc. London Ser A 264 (1969), 413–496. (1969) | MR 0282058 | Zbl 0181.38003

Makar-Limanov, L.G. Solution of Dirichlet’s problem for the equation Δu=-1 in a convex region, Math. Notes 9 (1971), 195–206. (1971) | MR 0279321 | Zbl 0222.31004

Whiteside, D.T. The Mathematical Papers of Isaac Newton – Vol. VI, Cambridge University Press, London, 1974. (1974) | MR 0505130 | Zbl 0296.01007

Talenti, G. Non linear elliptic equations, rearrangements of functions and Orlicz spaces, Ann. Mat. Pura Appl. (4) 120 (1977), 159–184. (1977) | MR 0551065

Feistaue, M.; Nečas, J. On the solvability of transonic potential flow problems, Z. Anal. Anwend. 4 (1985), 305–329. (1985) | MR 0807140

Chipot, M.; Evans, L.C. Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations, Proc. Roy. Soc. Edinburgh 102 A (1986), 291–303. (1986) | MR 0852362

Kawohl, B. On the location of maxima of the gradient for solutions to quasilinear elliptic problems and a problem raised by Saint Venant, J. Elasticity 17 (1987), 195–206. (1987) | MR 0888315 | Zbl 0624.73011

Kosmodem’yanskii Jr, A.A. The behaviour of solutions for the equationΔu=-1 in convex domains, Soviet Math. Dokl. 39 (1989), 112–114. (1989)

Sweers, G. A counterexample with convex domain to a conjecture of De Saint Venant, J. Elasticity 22 (1989), 57–61. (1989) | MR 1022331 | Zbl 0693.73005

Marcellini, P. Nonconvex integrals of the calculus of variations, Methods of Nonconvex Analysis, A. Cellina (ed.), Springer Lecture Notes in Math. 1446, 1990, pp. 16–57. (1990) | MR 1079758

Ramaswamy, M. A counterexample to the conjecture of Saint Venant by reflection methods, Differential Integral Equations 3 (1990), 653–662. (1990) | MR 1044211

Kawohl, B.; Stará, J.; Wittum, G. Analysis and numerical studies of a shape design problem, Arch. Rational Mech. Anal. 114 (1991), 349–363. (1991) | MR 1100800

Sweers, G. On examples to a conjecture of De Saint Venant, Nonlinear Anal. 18 (1992), 889–991. (1992) | MR 1162480 | Zbl 0794.73027

Buttazzo, G; Kawohl, B. On Newton’s problem of minimal resistance, Math. Intelligencer 15 (1993), no. 4, 7–12. (1993) | MR 1240664 | Zbl 0800.49038

Ferone, V.; Posteraro, M.R.; Volpicelli, R. An inequality concerning rearrangements of functions and Hamilton Jacobi equations, Arch. Rational Mech. Anal. 125 (1993), 257–269. (1993) | MR 1245072 | Zbl 0787.35020