# American Institute of Mathematical Sciences

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On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory
June  2020, 40(6): 3305-3325. doi: 10.3934/dcds.2020045

## Sectional symmetry of solutions of elliptic systems in cylindrical domains

 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  March 2019 Revised  June 2019 Published  October 2019

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

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].

Citation: Lucio Damascelli, Filomena Pacella. Sectional symmetry of solutions of elliptic systems in cylindrical domains. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3305-3325. doi: 10.3934/dcds.2020045
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##### References:
 [1] H. O. Fattorini. The maximum principle in infinite dimension. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 557-574. doi: 10.3934/dcds.2000.6.557 [2] Carlo Orrieri. A stochastic maximum principle with dissipativity conditions. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 5499-5519. doi: 10.3934/dcds.2015.35.5499 [3] Philip Korman. Infinitely many solutions and Morse index for non-autonomous elliptic problems. Communications on Pure & Applied Analysis, 2020, 19 (1) : 31-46. doi: 10.3934/cpaa.2020003 [4] Zongming Guo, Zhongyuan Liu, Juncheng Wei, Feng Zhou. Bifurcations of some elliptic problems with a singular nonlinearity via Morse index. Communications on Pure & Applied Analysis, 2011, 10 (2) : 507-525. doi: 10.3934/cpaa.2011.10.507 [5] Belgacem Rahal, Cherif Zaidi. On finite Morse index solutions of higher order fractional elliptic equations. Evolution Equations & Control Theory, 2021, 10 (3) : 575-597. doi: 10.3934/eect.2020081 [6] Torsten Lindström. Discrete models and Fisher's maximum principle in ecology. Conference Publications, 2003, 2003 (Special) : 571-579. doi: 10.3934/proc.2003.2003.571 [7] Mingshang Hu. Stochastic global maximum principle for optimization with recursive utilities. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 1-. doi: 10.1186/s41546-017-0014-7 [8] Matteo Negri. Crack propagation by a regularization of the principle of local symmetry. Discrete & Continuous Dynamical Systems - S, 2013, 6 (1) : 147-165. doi: 10.3934/dcdss.2013.6.147 [9] Linfeng Mei, Zongming Guo. Morse indices and symmetry breaking for the Gelfand equation in expanding annuli. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1509-1523. doi: 10.3934/dcdsb.2017072 [10] Yunkyong Hyon, Do Young Kwak, Chun Liu. Energetic variational approach in complex fluids: Maximum dissipation principle. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1291-1304. doi: 10.3934/dcds.2010.26.1291 [11] Chiun-Chuan Chen, Li-Chang Hung, Hsiao-Feng Liu. N-barrier maximum principle for degenerate elliptic systems and its application. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 791-821. doi: 10.3934/dcds.2018034 [12] Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195 [13] Tomasz Komorowski, Adam Bobrowski. A quantitative Hopf-type maximum principle for subsolutions of elliptic PDEs. Discrete & Continuous Dynamical Systems - S, 2020, 13 (12) : 3495-3502. doi: 10.3934/dcdss.2020248 [14] Yan Wang, Yanxiang Zhao, Lei Wang, Aimin Song, Yanping Ma. Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer. Journal of Industrial & Management Optimization, 2018, 14 (2) : 653-671. doi: 10.3934/jimo.2017067 [15] Shanjian Tang. A second-order maximum principle for singular optimal stochastic controls. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1581-1599. doi: 10.3934/dcdsb.2010.14.1581 [16] H. O. Fattorini. The maximum principle for linear infinite dimensional control systems with state constraints. Discrete & Continuous Dynamical Systems, 1995, 1 (1) : 77-101. doi: 10.3934/dcds.1995.1.77 [17] Isabeau Birindelli, Francoise Demengel. Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators. Communications on Pure & Applied Analysis, 2007, 6 (2) : 335-366. doi: 10.3934/cpaa.2007.6.335 [18] Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 395-415. doi: 10.3934/cpaa.2004.3.395 [19] Shaolin Ji, Xiaole Xue. A stochastic maximum principle for linear quadratic problem with nonconvex control domain. Mathematical Control & Related Fields, 2019, 9 (3) : 495-507. doi: 10.3934/mcrf.2019022 [20] Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020048

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