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Ambrosio, L; De Lellis, C; Mantegazza, C (1999). Line energies for gradient vector fields in the plane. Calculus of Variations and Partial Differential Equations, 9(4):327-255.
In this paper we study the singular perturbation of by . This problem, which could be thought as the natural second order version of the classical singular perturbation of the potential energy by , leads, as in the first order case, to energy concentration effects on hypersurfaces. In the two dimensional case we study the natural domain for the limiting energy and prove a compactness theorem in this class.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Physical Sciences > Applied Mathematics |
| Uncontrolled Keywords: | singular perturbation problems, energy concentration effects, eikonal equation, integral functional |
| Language: | English |
| Date: | 1999 |
| Deposited On: | 29 Nov 2010 16:27 |
| Last Modified: | 03 Dec 2024 02:39 |
| Publisher: | Springer |
| ISSN: | 0944-2669 |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1007/s005260050144 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1731470 |
Ambrosio, L