The article is concerned with qualitative properties of solutions of elliptic equations and systems. In particular, we address the question whether (some) solutions inherit the symmetry properties of the domain. By the well-known theorem of Gidas-Ni-Nirenberg one knows that the positive solutions of certain autonomous elliptic equations on radial domains are radial. On the other hand, for equations with weights this symmetry may be broken. We discuss related results for systems of such equations.
Qualitative properties of solutions of semilinear elliptic systems / M. Calanchi, B. Ruf - In: Recent trends on Nonlinear Elliptic Systems / G.A. Afrouzi, L. Boccardo ,M. Calanchi and B. Ruf , G.M. Figueiredo , S. El Manouni, J. P. Pinasco , J. Velin , D. A. Kandilakis and N. B. Zographopoulos ; [a cura di] N. Zographopoulos. - Athens, Greece : International ScientificPress, 2012. - ISBN 978-618-80003-0-8. - pp. 1-271
Qualitative properties of solutions of semilinear elliptic systems
M. CalanchiPrimo
;B. RufUltimo
2012
Abstract
The article is concerned with qualitative properties of solutions of elliptic equations and systems. In particular, we address the question whether (some) solutions inherit the symmetry properties of the domain. By the well-known theorem of Gidas-Ni-Nirenberg one knows that the positive solutions of certain autonomous elliptic equations on radial domains are radial. On the other hand, for equations with weights this symmetry may be broken. We discuss related results for systems of such equations.
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