|Title||Line energies for gradient vector fields in the plane|
|Publication Type||Journal Article|
|Year of Publication||1999|
|Authors||Ambrosio L., De Lellis C., Mantegazza C.|
|Journal||Calculus of Variations and Partial Differential Equations|
|Type of Article||phase|
|Keywords||eikonal equation, energy concentration effects, integral functional, singular perturbation problems|
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.
Calc. Var. Partial Differential Equations 9 (1999), no. 4, 327–255.