Geodesic
A paradox in the theory of linear elasticity
Applications of Mathematics, Tome 21 (1976) no. 6, pp. 431-433
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Let us have the system of partial differential equations of the linear elasticity. We show that the solution of this system with a bounded boundary condition is not generally bounded (i.e., the displacement vector is not bounded). This example is a modification of that given by E. De Giorgi [1].
Let us have the system of partial differential equations of the linear elasticity. We show that the solution of this system with a bounded boundary condition is not generally bounded (i.e., the displacement vector is not bounded). This example is a modification of that given by E. De Giorgi [1].
DOI : 10.21136/AM.1976.103667
Classification : 74E05
Keywords: nonhomogeneous linear elastic medium 
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Nečas, Jindřich; Štípl, Miloš. A paradox in the theory of linear elasticity. Applications of Mathematics, Tome 21 (1976) no. 6, pp. 431-433. doi: 10.21136/AM.1976.103667

[1] E. De Giorgi: Un essempio di estremali discontinue per un problema variazionele di tipo ellitico. Boll. U. M. I., Vol. I., 1968, 135-137. | MR

[2] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Praha 1967. | MR

[3] L. F. Nye: Physical properties of crystals. Oxford 1957. | Zbl

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