## Some remarks on nonuniqueness of minimizers for discrete minimization problems.(English)Zbl 1009.49026

The authors approximate the variational problem $\int\varphi(\nabla v(x)) dx\to \inf_{v\in W^{1,\infty}_0(\Omega)}$ by finite elements and show that when the continuous problem does not admit a minimizer its approximation may lead to several discrete minimizers.

### MSC:

 49M25 Discrete approximations in optimal control 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 49J10 Existence theories for free problems in two or more independent variables

### Keywords:

variational problem; finite elements; discrete minimizers
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### References:

 [1] Brighi B., SIAM J. Numer. Anal. 31 (1) pp 128– (1994) · Zbl 0796.65009 [2] Chipot M., Numer. Math. 59 pp 747– (1991) · Zbl 0712.65063 [3] Chipot M., Numer. Math. 83 (3) pp 325– (1999) · Zbl 0937.65070 [4] Chipot M., SIAM J. Numer. Anal. 29 (4) pp 473– (1993) [5] Chipot M., Numer. Math. 70 pp 259– (1995) · Zbl 0824.65045 [6] Chipot M., Japan J. Indust. Appl. Math. 15 pp 345– (1998) · Zbl 0922.65049 [7] DOI: 10.1007/BF00251759 · Zbl 0673.73012 [8] Friesecke G., Proc. Roy. Soc. Edinburgh Sect. A 124 pp 437– (1994) [9] Kohn R. V., Philos. Mag. Ser. A 66 pp 697– (1992)
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