The singular homogeneous solutions to one phase free boundary problem
The singular homogeneous solutions to one phase free boundary problem
We provide some new examples of singular homogeneous of degree one solutions to the well-known one phase free boundary problem. They are critical points of the functional $J(v,B)=\int _B |\nabla v|^2+\chi _{\{v>0\}}$. We also discuss their stability using a criteria of Caffarelli, Jerison and Kenig.