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Friends in Partial Differential Equations
May 24, 2024 15:15, St. Petersburg, St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, online


Uniform (or not) a priori estimates for the Lane-Emden system in the plane

B. Sirakov

Pontifical Catholic University of Rio de Janeiro



Abstract: We prove that positive solutions of the superlinear Lane-Emden system in a two-dimensional smooth bounded domain are bounded independently of the exponents in the system, provided the exponents are comparable. As a consequence, the energy of the solutions is uniformly bounded, a crucial information in their asymptotic study.
On the other hand, the boundedness may fail if the exponents are not comparable, a surprising incidence of a situation in which the sub-critical Lane-Emden system behaves differently from the scalar Lane-Emden equation.
Joint work with Nikola Kamburov (PUC-Chile).

Language: English


© Steklov Math. Inst. of RAS, 2024