Line energies for gradient vector fields in the plane
- 163 Downloads
In this paper we study the singular perturbation of \(\int (1-|\nabla u|^2)^2\) by \(\varepsilon^2|\nabla^2u|^2\). This problem, which could be thought as the natural second order version of the classical singular perturbation of the potential energy \(\int (1-u^2)^2\) by \(\varepsilon^2|\nabla u|^2\), 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.
KeywordsPotential Energy Vector Field Energy Concentration Concentration Effect Dimensional Case
Unable to display preview. Download preview PDF.