December  2015, 35(12): 5609-5629. doi: 10.3934/dcds.2015.35.5609

Harmonic functions in union of chambers

1. 

Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi, 55 - 20125 Milano, Italy

2. 

Dipartimento di Matematica "Giuseppe Peano", Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino

Received  March 2014 Published  May 2015

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.
Citation: Laura Abatangelo, Susanna Terracini. Harmonic functions in union of chambers. Discrete & Continuous Dynamical Systems, 2015, 35 (12) : 5609-5629. doi: 10.3934/dcds.2015.35.5609
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show all references

References:
[1]

Journal of Functional Analysis, 266 (2014), 3632-3684. doi: 10.1016/j.jfa.2013.11.019.  Google Scholar

[2]

Journal of Differential Equations, 256 (2014), 3301-3334. doi: 10.1016/j.jde.2014.02.010.  Google Scholar

[3]

Academic Press 2003.  Google Scholar

[4]

Netw. Heterog. Media, 2 (2007), 761-777. doi: 10.3934/nhm.2007.2.761.  Google Scholar

[5]

ESAIM Control Optim. Calc. Var., 12 (2006), 752-769. doi: 10.1051/cocv:2006020.  Google Scholar

[6]

Arch. Rational Mech. Anal., 65 (1977), 275-288. doi: 10.1007/BF00280445.  Google Scholar

[7]

J. Differential Equations, 255 (2013), 633-700. doi: 10.1016/j.jde.2013.04.017.  Google Scholar

[8]

Springer, 2001. Google Scholar

[9]

Springer, 2006.  Google Scholar

[10]

Adv. in Math., 46 (1982), 80-147. doi: 10.1016/0001-8708(82)90055-X.  Google Scholar

[11]

Springer-Verlag, 1995.  Google Scholar

[12]

Springer, 1996. doi: 10.1007/978-1-4612-5338-9.  Google Scholar

[13]

Publ. Res. Inst. Math. Sci., 26 (1990), 585-627. doi: 10.2977/prims/1195170848.  Google Scholar

[14]

Duke Math. J., 57 (1988), 955-980. doi: 10.1215/S0012-7094-88-05743-2.  Google Scholar

[15]

in Maximum Principles and Eigenvalue Problems in Partial Differential Equations (Knoxville, TN, 1987), Pitman Res. Notes Math. Ser., 175, Longman Sci. Tech., Harlow, 1988, 218-230.  Google Scholar

[16]

Ann. Inst.H. Poincaré Anal. Non Linéaire, 11 (1994), 313-341.  Google Scholar

[17]

Cambridge Studies in Advanced Mathematics, 45, Cambridge University Press, Cambridge, 1995. doi: 10.1017/CBO9780511526244.  Google Scholar

[18]

Springer, 1984. doi: 10.1007/978-1-4612-5282-5.  Google Scholar

[19]

McGraw-Hill, 1987.  Google Scholar

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