Free access
Issue
ESAIM: COCV
Volume 6, 2001
Page(s) 517 - 538
DOI http://dx.doi.org/10.1051/cocv:2001121
Published online 15 August 2002
  1. L. Ambrosio, A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. B 3 (1989) 857-881. [MathSciNet]
  2. L. Ambrosio, Existence theory for a new class of variational problems. Arch. Rational Mech. Anal. 111 (1990) 291-322. [CrossRef] [MathSciNet]
  3. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Clarendon Press, Oxford (2000).
  4. L. Ambrosio and V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Formula -convergence. Comm. Pure Appl. Math. 43 (1990) 999-1036. [CrossRef] [MathSciNet]
  5. L. Ambrosio and V.M. Tortorelli, On the approximation of free discontinuity problem. Boll. Un. Mat. Ital. B 6 (1992) 105-123. [MathSciNet]
  6. A. Blake and A. Zisserman, Visual Reconstruction. The MIT Press, Cambridge Mass, London (1987).
  7. E. Bonnetier and M. Vogelius, An elliptic regularity result for a composite medium with ``touching'' fibers of circular cross-section. SIAM J. Math. Anal. 31 (2000) 651-677. [CrossRef] [MathSciNet]
  8. A. Braides, Approximation of Free-Discontinuity Problems. Springer-Verlag, Berlin Heidelberg New York (1998).
  9. A.P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics. Sociedade Brasileira de Matemática, Rio de Janeiro (1980) 65-73.
  10. G. Congedo and I. Tamanini, On the existence of solutions to a problem in multidimensional segmentation. Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 175-195.
  11. G. Dal Maso, An Introduction to Formula -convergence. Birkhäuser, Boston Basel Berlin (1993).
  12. E. De Giorgi, M. Carriero and A. Leaci, Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal. 108 (1989) 195-218. [CrossRef] [MathSciNet]
  13. D.C. Dobson, Stability and Regularity of an Inverse Elliptic Boundary Value Problem, Ph.D. Thesis. Rice University, Houston (1990).
  14. D.C. Dobson and F. Santosa, An image-enhancement technique for electrical impedance tomography. Inverse Problems 10 (1994) 317-334. [CrossRef] [MathSciNet]
  15. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton Ann Arbor London (1992).
  16. V. Isakov, Inverse Problems for Partial Differential Equations. Springer-Verlag, New York Berlin Heidelberg (1998).
  17. E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston Basel Stuttgart (1984).
  18. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. Academic Press, New York London Toronto (1980).
  19. R.V. Kohn and M. Vogelius, Determining conductivity by boundary measurements. Comm. Pure Appl. Math. 37 (1984) 289-298. [CrossRef] [MathSciNet]
  20. Y.Y. Li and M. Vogelius, Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients. Arch. Rational Mech. Anal. 153 (2000) 91-151. [CrossRef]
  21. N.G. Meyers, An Lp-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (1963) 189-205.
  22. D. Mumford and J. Shah, Boundary detection by minimizing functionals, I, in Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Press/North-Holland, Silver Spring Md./Amsterdam (1985) 22-26.
  23. D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42 (1989) 577-685. [CrossRef] [MathSciNet]
  24. J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125 (1987) 153-169. [CrossRef] [MathSciNet]
  25. G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems. Plenum Press, New York London (1987).