| Abstract: |
| The Lane-Emden system is an extremal equation associated with a specific Sobolev embedding, and it is closely related to the Calderon-Zygmund estimates. This system is one of the simplest elliptic Hamiltonian systems, as the nonlinear Schroedinger system is that of elliptic gradient systems.
In this talk, we examine recent developments in the theory of the Lane-Emden system. This includes discussions on slightly subcritical Lane-Emden systems on smooth bounded domains and the critical Lane-Emden system on the entire Euclidean space or smooth bounded domains with small spherical holes. |
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