Uniform a priori estimates for positive solutions of the Lane-Emden system in the plane

Nikola Kamburov; Boyan Sirakov

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arXiv · 2205.02587

Uniform a priori estimates for positive solutions of the Lane-Emden system in the plane

Nikola Kamburov·Boyan Sirakov

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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. In addition, the boundedness may fail if the exponents are not comparable.

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Nikola Kamburov, Boyan Sirakov. 2022-05-05. Uniform a priori estimates for positive solutions of the Lane-Emden system in the plane. https://arxiv.org/abs/2205.02587

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