We characterize the set of harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of two different chambers. We analyse the asymptotic behavior of the solutions in connection with the changes in the domain's geometry; we classify all (possibly sign-changing) infinite energy solutions having given asymptotic frequency at the infinite ends of the domain; finally we sketch the case of several different chambers.
Abatangelo, L., Terracini, S. (2015). Harmonic functions in union of chambers. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 35(12), 5609-5629 [10.3934/dcds.2015.35.5609].
Harmonic functions in union of chambers
ABATANGELO, LAURA;
2015
Abstract
We characterize the set of harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of two different chambers. We analyse the asymptotic behavior of the solutions in connection with the changes in the domain's geometry; we classify all (possibly sign-changing) infinite energy solutions having given asymptotic frequency at the infinite ends of the domain; finally we sketch the case of several different chambers.
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