References
Alexandrov, A. D., Uniqueness theorems for surfaces in the large, part V. Vestnik Leningrad University 13 (1958) p. 5–8.
Bauman, P., & D. Phillips, A nonconvex variational problem related to change of phase. Appl. Math. Optim. 21 (1990) p. 113–138.
Buononcore, P., Some isoperimetric inequalities in a special case of the problem of torsional creep. Applic. Anal. 27 (1988) pp. 133–142.
Chipot, M., & L. C. Evans, Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations. Proc. Roy. Soc. Edinburgh 102 A (1986) pp. 291–303.
Dacorogna, B., Direct methods in the calculus of variations. Springer (1989) Berlin.
French, D., On the convergence of finite element approximations of relaxed variational problem. IMA Preprint 503, Minneapolis 1989.
Giaquinta, M., & E. Giusti, On the regularity of the minima of variational integrals. Acta Math. 148 (1982) pp. 31–46.
Goodman, J., Kohn, V. R., & L. Reyna, Numerical study of a relaxed variational problem from optimal design. Computer Methods in Applied Math. and Engin. 57 (1986) pp. 107–127.
Hackbusch, W., Multi-grid methods. Springer-Verlag (1985) Heidelberg.
Hackbusch, W., Theorie und Numerik elliptischer Differentialgleichungen. Teubner-Verlag (1986) Stuttgart.
Hackbusch, W., & A. Reusken, Analysis of a damped nonlinear multilevel method. Numer. Math. 55 (1989) pp. 225–246.
Hoppe, R., & R. Kornhuber, Multi-grid methods for the two phase Stefan problem. Report 171, Techn. Univ. Berlin (1987).
Kawohl, B., Rearrangements and convexity of level sets in PDE. Springer Lecture Notes in Math. 1150 (1985) Heidelberg.
Kohn, R., & G. Strang, Optimal design and relaxation of variational problems I, II, III. Comm. Pure Appl. Math. 39 (1986) pp. 113–137, 139–182, 353–377.
Lurie, K. A., A. V. Cherkaev & A. V. Fedorov, Regularization of optimal design problems for bars and plates. J. Optim. Theory Appl. 37 (1982) pp. 499–543.
Murat, F., & L. Tartar, Optimality conditions and homogenization, in: Nonlinear Variational Problems. Eds.: A. Marino, L. Modica, S. Spagnolo & M. Degiovanni, Pitman Research Notes in Math. 127 (1985) pp. 1–8.
Murat, F., & L. Tartar, Calcul des variations et homogenization, in: Les méthodes de l'homogeneisation: théorie et applications en physique. Eds.: D. Bergman et al. Collection de la Direction des Études et Recherches d'Electricité de France 57 (1985) pp. 319–369.
Talenti, G., Non linear elliptic equations, rearrangements of functions and Orlicz spaces. Ann. Mat. Pura Appl. Ser. IV 120 (1977) pp. 159–184.
Voas, C., & D. Yaniro, Symmetrization and optimal control for elliptic equations. Proc. Amer. Math. Soc. 99 (1987) pp. 509–514.
Wittum, G., Linear iterations as smoothers in multigrid methods: Theory with applications to incomplete decompositions. Impact of Computing in Science and Engineering 1 (1989) pp. 180–215.
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Communicated by R. V. Kohn
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Kawohl, B., Stara, J. & Wittum, G. Analysis and numerical studies of a problem of shape design. Arch. Rational Mech. Anal. 114, 349–363 (1991). https://doi.org/10.1007/BF00376139
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DOI: https://doi.org/10.1007/BF00376139