PDE och tillämpningar: Free boundary regularity for the p-harmonic obstacle problem

Abstract: We will consider the following problem

$$

\Delta_p u= \chi_{\{u>0\}} \textrm{ in }\mathcal{D},

$$

where $\mathcal{D}$ is some given domain and $\Delta_p$ is the p-harmonic operator for some $p\ge 2$. We will show a standard regularity result for the boundary $\Gamma=\partial \{u>0\}\cap \mathcal{D}$: that $\Gamma$ is $C^{1,\alpha}$ on an open set of full measure.