By Joyner D., Kreminski R., Turisco J.
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However, the weak limit of uε in the sense of the bounds (45), (47) will satisfy (6) in the sense of distributions. The boundary conditions (7), (8) are obtained easily by considering the limits of uε+ χ+ (y) + β+ (y) and uε− χ− (y) + β(y) which amount to considering the limits of the numbers uε+ , uε− which are bounded by λg . So we can extract converging subsequences. This is also the trace of a converging subsequence of uε . The proof has been completed. Acknowledgement. This research was partially supported by a grant from CEA, Commissariat ` a l’´energie atomique and by the National Science Foundation under grant DMS-0705247.
50 J. Tambaˇca et al. stent (at 2–4 points in the center) and to the end points (at 1 point near each end of a stent). The force at the end points is applied in the opposite direction from the force applied to the center of the stent.
Cliﬀ, and S. Schreck, editors, Computational Methods for Optimal Design and Control, Proceedings of the AFOSR workshop on Optimal Design and Control (Arlington, VA, 1997), pages 151–179. Birkh¨ auser, 1998. 8. M. D. Gunzburger. Perspectives in ﬂow control and optimization. SIAM, Philadelphia, PA, 2003. 9. M. E. Gurtin. An introduction to continuum mechanics. Academic Press, 2003. 10. J. Haslinger and R. A. E. M¨ akinen. Introduction to shape optimization. Theory, approximation, and computation.
Applied abstract algebra by Joyner D., Kreminski R., Turisco J.