Harmonic functions in union of chambers

Laura  Abatangelo; Susanna Terracini

doi:10.3934/dcds.2015.35.5609

Article Contents

2015, Volume 35, Issue 12: 5609-5629. Doi: 10.3934/dcds.2015.35.5609

This issue Previous Article Large $s$-harmonic functions and boundary blow-up solutions for the fractional Laplacian Next Article Density estimates for vector minimizers and applications

Harmonic functions in union of chambers

Laura Abatangelo^1, and
Susanna Terracini^2,

1.
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi, 55 - 20125 Milano
2.
Dipartimento di Matematica "Giuseppe Peano", Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino

Received: February 28, 2014

Published: November 2015

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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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Mathematics Subject Classification: Primary: 35B40, 35J25, 35P15, 35B20.

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