Critical points of Laplace eigenfunctions on polygons

Judge, C. and Mondal, S. ORCID: https://orcid.org/0000-0002-2236-971X (2022) Critical points of Laplace eigenfunctions on polygons. Communications in Partial Differential Equations, 47 (8). pp. 1559-1590. ISSN 1532-4133 doi: 10.1080/03605302.2022.2062572

Abstract/Summary

We study the critical points of Laplace eigenfunctions on polygonal domains with a focus on the second Neumann eigenfunction. We show that if each convex quadrilaterals has no second Neumann eigenfunction with an interior critical point, then there exists a convex quadrilateral with an unstable critical point. We also show that each critical point of a second-Neumann eigenfunction on a Lip-1 polygon with no orthogonal sides is an acute vertex.