Uniform cusp property, boundary integral, and compactness for shape optimization

IFIP Advances in Information and Communication Technology

Volumn 166, Issue , 2005, Pages 25-40

  Delfour, Michel C ^a   Doyon, Nicolas ^a   Zolésio, Jean Paul ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b CNRS   (France)

Author keywords

Boundary integral; Compactness; Cusp property; Density perimeter; Hausdorff dimension; Oriented distance function; Signed distance function

Indexed keywords

FRACTALS;

BOUNDARY INTEGRALS; COMPACTNESS; CUSP PROPERTY; DISTANCE FUNCTIONS; HAUSDORFF DIMENSION; SIGNED DISTANCE FUNCTION;

SHAPE OPTIMIZATION;

EID: 84902474508     PISSN: 18684238     EISSN: None     Source Type: Book Series    
DOI: 10.1007/0-387-23467-5_2     Document Type: Conference Paper

References (6)

1. D. Bucur and J.-P. ZolCsio, Free boundary problems and density perimeter, J. Differential Equations 126 (1996), 224-243.
2. M. C. Delfour and J.-P. ZolBsio, Shapes and Geometries: Analysis, Differential Calculus and Optimization, SIAM series on Advances in Design and Control, Society for Industrial and Applied Mathematics, Philadelphia, USA 2001.
3. M. C. Delfour and J.-P. ZolBsio, The new family of cracked sets and the image segmentation problem revisited, CRM Report, May 2003, UniversitC de MontrCal, accepted in Communications in Information and Systems.
4. M. C. Delfour, N. Doyon, and J.-P. ZolBsio, Extension of the uniform cusp property in shape optimization, in "Control of Partial Differential Equations, " G. Leugering, O. Imanuvilov, R. Triggiani, and B. Zhang, eds. Lectures Notes in Pure and Applied Mathematics, Marcel Dekker, May 2003, accepted.
5. M. C. Delfour, N. Doyon, and J.-P. ZolCsio, The uniform fat segment and cusp properties in shape optimization, in "Control and Boundary analysis, " J. Cagnol and J.-P. ZolCsio (Eds.), pp. 85-96, Marcel Dekker 2004.
6. E. Giusti, Minimal surfaces and functions of bounded variation, Birkhauser, Boston, Basel, Stuttgart, 1984.