Sectional symmetry of solutions of elliptic systems in cylindrical domains

Lucio Damascelli; Filomena Pacella

doi:10.3934/dcds.2020045

Article Contents

2020, Volume 40, Issue 6: 3305-3325. Doi: 10.3934/dcds.2020045 open access

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$ \mathbb{R}^4 $

Sectional symmetry of solutions of elliptic systems in cylindrical domains

Lucio Damascelli^1, and
Filomena Pacella^2,

1.
Dipartimento di Matematica, Università di Roma, "Tor Vergata" - Via della Ricerca Scientifica 1 - 00133 Roma, Italy
2.
Dipartimento di Matematica, Università di Roma, "Sapienza" - P.le A. Moro 2 - 00185 Roma, Italy

Received: February 28, 2019

Revised: May 31, 2019

Published: March 2020

The first author acknowledges the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006

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Abstract

In this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains. The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy some convexity assumptions. These results extend and improve those obtained in [6,9,16,18].

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Mathematics Subject Classification: Primary: 3502, 35J61, 35P99; Secondary: 35B06, 35B07, 35B50.

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References

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