Symmetry-breaking bifurcations for free boundary problems Andrei BorisovichAvner Friedman Free boundary problems often possess solutions which are radially symmetric. In this paper we demonstrate how to establish sim\-me\-try-breaking bifurcation branches of solutions by reducing the bifurcation problem to one for which standard bifurcation theory can be applied. This reduction is performed by first introducing a suitable diffeomorphism which maps the near circular unknown domain onto a disc or a ball, and then verifying the assumptions of the Crandall-Rabinowitz theorem. We carry out the analysis in detail, for the case of one elliptic equation with a Neumann condition at the free boundary and with Dirichlet data given by the curvature of the free boundary. Other examples are briefly mentioned. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2473 10.1512/iumj.2005.54.2473 en Indiana Univ. Math. J. 54 (2005) 927 - 947 state-of-the-art mathematics http://iumj.org/access/