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Exponential dichotomies for elliptic PDE on radial domains
Margaret Beck, Graham Cox, Christopher Jones +2
It was recently shown by the authors that a semilinear elliptic equation can be represented as an infinite-dimensional dynamical system in terms of boundary data on a shrinking one…
A dynamical approach to semilinear elliptic equations
Margaret Beck, Graham Cox, Christopher Jones +2
A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in is given in terms of an infinite-dimensional dynamical system.…
Isoperimetric relations between Dirichlet and Neumann eigenvalues
Graham Cox, Scott Scott MacLachlan, Luke Steeves
Inequalities between the Dirichlet and Neumann eigenvalues of the Laplacian have received much attention in the literature, but open problems abound. Here, we study the number of N…
Conformal invariants from nodal sets II. Manifolds with boundary
Graham Cox, Dmitry Jakobson, Mikhail Karpukhin +1
In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators on manifolds with boundary. We also consider app…