Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems

Communications on Pure and Applied MathematicsVolume 42, Issue 5 p. 577-685 Article Optimal approximations by piecewise smooth functions and associated variational problems† David Mumford, David Mumford Harvard UniversitySearch for more papers by this authorJayant Shah, Jayant Shah Northeastern UniversitySearch for more papers by this author David Mumford, David Mumford Harvard UniversitySearch for more papers by this authorJayant Shah, Jayant Shah Northeastern UniversitySearch for more papers by this author First published: July 1989 https://doi.org/10.1002/cpa.3160420503Citations: 3,727 † A preliminary version of this paper was submitted by invitation in 1986 to „Computer Vision 1988”︁, L. Erlbaum Press, but it has not appeared! AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Allard, W. K., and Almgren, F. J., The structure of stationary one-dimensional varifolds with positive density, Inventiones Math. 34, 1976, pp. 83–97. 2 M. Abramowitz, and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series, 1965. 3 Buser, P., On Cheeger's inequality, Proc. of Symp. in Pure Math. 36, 1980. 4 Blake, A., and Zisserman, A., Using Weak Continuity Constraints, Report CSR-186–85, Dept. of Comp. Sci., Edinburgh University, 1985. 5 Freidlin, M., Functional Integration and Partial Differential Equations, Annals of Math. Studies, Princeton University Press, 1985. 6 Geman, S., and Geman, D., Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans., PAMI 6, 1984, pp. 721–741. 7 Grisvard, P., Elliptic Problems in Nonsmooth Domains, Pitman, 1985. 8 Gurtin, M. E., On a theory of phase transitions with interfacial energy, Archive Rat. Mech. Anal. 87, 1985, pp. 187–212. 9 Kondratiev, V. A., Boundary value problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc. 16, 1967, pp. 227–313. 10 Marroquin, J. L., Surface reconstruction preserving discontinuities, Artificial Intelligence Lab. Memo 792, M.I.T., 1984. 11 McKean, H., Stochastic Integrals, Academic Press, 1969. 12 Rice, J. R., Mathematical analysis in the mechanics of fracture, in Fracture, An Advanced Treatise, H. Liebowitz, ed., Academic Press, 1968. 13 Simon, L., Lectures on Geometric Measure Theory, Proc. Centre for Math. Anal., Australian Nat. Univ., 3, 1983. 14 Whittaker, E. T., and Watson, G. N., A Course of Modern Analysis, 4th ed., Cambridge University Press, 1952. Citing Literature Volume42, Issue5July 1989Pages 577-685 ReferencesRelatedInformation