We study the bifurcation structure to Serrin’s overdetermined problem such that
We prove that the bifurcation from the straight cylinder with is critical at the bifurcation point. Moreover, we obtain the global structure of bifurcation branches. To study the global structure of bifurcation branches, we establish a global bifurcation theorem in finite dimensional space.
"BIFURCATION STRUCTURE TO SERRIN’S OVERDETERMINED PROBLEM." Rocky Mountain J. Math. 53 (5) 1445 - 1458, October 2023. https://doi.org/10.1216/rmj.2023.53.1445