Publication: Line energies for gradient vector fields in the plane
Line energies for gradient vector fields in the plane
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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. https://doi.org/10.1007/s005260050144
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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.
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- Ambrosio, L
- De Lellis, C
- Mantegazza, C
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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. https://doi.org/10.1007/s005260050144