Regularity of the Eikonal equation with two vanishing entropies

Andrew Lorent, Guanying Peng

The Aviles-Giga functional $I_{\epsilon }(u)={\int }_{\Omega }\frac{{|1-{|\nabla u|}^2|}^2}{\epsilon }+\epsilon {\left|{\nabla }^{2}u\right|}^{2}dx$ is a well known second order functional that models phe…