| Title:
|
On the shape of solutions to some variational problems (English) |
| Author:
|
Kawohl, Bernd |
| Language:
|
English |
| Journal:
|
Nonlinear Analysis, Function Spaces and Applications |
| Volume:
|
Vol. 5 |
| Issue:
|
1994 |
| Year:
|
|
| Pages:
|
77-102 |
| . |
| Category:
|
math |
| . |
| MSC:
|
49-02 |
| MSC:
|
49J40 |
| MSC:
|
49J45 |
| MSC:
|
49Q10 |
| MSC:
|
49Q20 |
| MSC:
|
73C10 |
| MSC:
|
74G50 |
| MSC:
|
74P99 |
| idZBL:
|
Zbl 0841.49022 |
| idMR:
|
MR1322310 |
| . |
| Date available:
|
2009-10-08T09:44:56Z |
| Last updated:
|
2012-08-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702460 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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[BK] Buttazzo, G, Kawohl, B.: On Newton’s problem of minimal resistance.Math. Intelligencer 15 (1993), no. 4, 7–12. Zbl 0800.49038, MR 1240664 |
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| Reference:
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[FPV] 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. Zbl 0787.35020, MR 1245072 |
| Reference:
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| Reference:
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[K] 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. Zbl 0624.73011, MR 0888315 |
| Reference:
|
[KS] 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.. Zbl 0908.65052, MR 1492052 |
| Reference:
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[KSW] Kawohl, B., Stará, J., Wittum, G.: Analysis and numerical studies of a shape design problem.Arch. Rational Mech. Anal. 114 (1991), 349–363. MR 1100800 |
| Reference:
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[Ko] Kosmodem’yanskii Jr, A.A.: The behaviour of solutions for the equation$\Delta u=-1$ in convex domains.Soviet Math. Dokl. 39 (1989), 112–114. |
| Reference:
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[M] 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. MR 1079758 |
| Reference:
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[ML] Makar-Limanov, L.G.: Solution of Dirichlet’s problem for the equation $\Delta u=-1$ in a convex region.Math. Notes 9 (1971), 195–206. Zbl 0222.31004, MR 0279321 |
| Reference:
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[N] Newton, I.: Philisophiae Naturalis Principia Mathematica.1686. |
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[Po] Polya, G.: Liegt die Stelle der größten Beanspruchung an der Oberfläche?.Z. Angew. Math. Mech. 10 (1930), 353–360. |
| Reference:
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| Reference:
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[R] Ramaswamy, M.: A counterexample to the conjecture of Saint Venant by reflection methods.Differential Integral Equations 3 (1990), 653–662. MR 1044211 |
| Reference:
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[Se] 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. Zbl 0181.38003, MR 0282058 |
| Reference:
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[S1] Sweers, G.: A counterexample with convex domain to a conjecture of De Saint Venant.J. Elasticity 22 (1989), 57–61. Zbl 0693.73005, MR 1022331 |
| Reference:
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| Reference:
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[SV] 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. |
| Reference:
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| . |
