An Energy Approach to Relative Overdetermined Problems – Part II

Rigidity and symmetry notions have aroused the interest of the mathematical community for a long time. In particular, since the seminal works of Serrin and Gidas, Ni, and Nirenberg, much effort has been devoted to understanding rigidity and symmetry-breaking phenomena for nonlinear elliptic equations in the radial setting. In this seminar, we discuss (somewhat) similar problems in a different geometric setting, namely, bounded cylinders. We show that, under quite weak assumptions, elementary bifurcation theory gives rise to a plethora of new, non-symmetric solutions, bifurcating from symmetric ones.