Semicontinuity and relaxation properties of a curvature depending functional in 2D

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1. [1] M. Berger - B. Gostiaux, Differential Geometry: Manifolds, Curves and Surfaces, Springer-Verlag, New York, 1988. Zbl0629.53001MR917479
2. [2] G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Longman Scientific & Technical, Harlow, 1989. Zbl0669.49005MR1020296
3. [3] H. Cartan, Théorie Elémentaire des Fonctions Analytiques d'Une ou Plusieurs Variables Complexes, Hermann, Paris, 1961. Zbl0094.04401MR147623
4. [4] E. De Giorgi, Some remarks on Γ-convergence and least squares method, in Proc. Composite media and homogenization theory (Trieste, 1990, G. Dal Maso, G.F. Dell'Antonio, eds.), Birkhäuser, Boston, 1991, pp. 135-142. Zbl0747.49008
5. [5] M.P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, New Jersey, 1976. Zbl0326.53001MR394451
6. [6] J.P. Duggan, W2,p regularity for varifolds with mean curvature, Comm. Partial Differential Equations, 11 (1986), pp. 903-926. Zbl0634.35022MR844169
7. [7] J.P. Duggan, Regularity theorems for varifolds with mean curvature, Indiana Univ. Math. J., 35 (1986), pp. 117-144. Zbl0595.49029MR825631
8. [8] L. Euler, Additamentum I de curvis elasticis, methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, Opera omnia, Lausanne, I24 (1744), pp. 231-297. 
9. [9] H. Federer, Geometric Measure Theory, Springer-Verlag, Berlin, 1968. Zbl0176.00801MR257325
10. [10] P. Funk, Variationsrechnung und ihre Anwendung in Physik und Technik, Springer-Verlag, Berlin. 1962. Zbl0119.09101MR152914
11. [11] D. Gilbarg - N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
12. [12] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Boston, 1984. Zbl0545.49018MR775682
13. [13] J.E. Hutchinson, Second fundamental form for varifolds and the existence of surfaces minimizing curvature, Indiana Univ, Math. J., 35 (1986), pp. 45-71. Zbl0561.53008MR825628
14. [14] A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover, New York, 1944. Zbl0063.03651MR10851
15. [15] D. Mumford - M. Nitzberg, The 2.1-D sketch, in Proc. European Conference on Computer Vision (1990). 
16. [16] O. Ore, Theory of Graphs, American Mathematical Society Colloquium Publications (XXXVIII), Providence, Rhode Island, 1962. Zbl0105.35401MR150753
17. [17] R.C. Penner, An Introduction to train tracks, in Low dimensional topology and Kleinian groups Edited by D.B.A. Epstein, London Math. Soc., Lecture Notes Ser., Cambridge Univ. Press.Cambridge-New York. Zbl0623.57005MR903859
18. [18] L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre of Mathematical Analysis, Canberra, 3, 1984. Zbl0546.49019MR756417
19. [19] W.P. Thurtson, The Geometry and Topology of 3-Manifolds, Princeton Univ. Press, Princeton1979. 

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