A minimum problem associated with scalar Ginzburg-Landau equation and free boundary

Yuwei Hu, Jun Zheng, Leandro S. Tavares

Let $N>2$, $p\in \left(\frac{2N}{N+2},+\infty \right)$, and $\Omega$ be an open bounded domain in ${\mathbb{R}}^N$. We consider the minimum problem $$ \mathcal{J} (u) := \displaystyle\int_…