Abstract: In the study of elliptic PDEs, symmetry properties of solutions are a classical topic. In this talk, we revisit this topic from a functional analytic perspective. Using properties of group actions on Sobolev spaces combined with some simple variational tools, we investigate elliptic operators on symmetric domains with a generalised (possibly non-local) Robin boundary condition. Our methods yield some surprising insights into the positivity of the ground state and the asymptotic behaviour of the associated heat equation.
This is joint work with Jochen Glück (Wuppertal).
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