• Corpus ID: 119641787

A geometric approach to regularity for nonlinear free boundary problems

@article{Karakhanyan2017AGA,
  title={A geometric approach to regularity for nonlinear free boundary problems},
  author={Aram L. Karakhanyan},
  journal={arXiv: Analysis of PDEs},
  year={2017}
}
  • A. Karakhanyan
  • Published 1 February 2017
  • Mathematics
  • arXiv: Analysis of PDEs
Let $u$ be a weak solutions of the free boundary problem $\mathcal L u=\lambda_0 \mathcal H^1\lfloor\partial\{u>0\}, u\ge 0$ where $\mathcal L u=\hbox{div}(g(\nabla u)\nabla u)$ and $g(\xi)$ is a given function of $\xi$ satisfying some standard structural conditions. We prove that the free boundary of the weak solutions is continuously differentiable in $\mathbb R^2$. The full regularity of the free boundary is not fully understood even for the $ minimizers$ in the simplest case $g(\xi)=|\xi… 

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