We consider the solution u to a semilinear elliptic boundary value problem with Dirichlet boundary condition on an annular planar domain with corners. We prove that u possesses a finite number of critical points and at most one critical curve. For certain annular domains having a regular n–gon as an outer boundary, we rule out the existence of critical curves.
CITATION STYLE
Arango, J., & Delgado, J. (2015). Critical points of solutions to elliptic equations in planar domains with corners. In Springer Proceedings in Mathematics and Statistics (Vol. 121, pp. 105–112). Springer New York LLC. https://doi.org/10.1007/978-3-319-12583-1_7
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