American Institute of Mathematical Sciences

December  2013, 18(10): 2505-2512. doi: 10.3934/dcdsb.2013.18.2505

Trudinger-Moser type inequality for radially symmetric functions in a ring and applications to Keller-Segel in a ring

 1 Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

Received  April 2013 Revised  July 2013 Published  October 2013

We prove that for radially symmetric functions in a ring $\Omega =${$x \in \mathbb{R}^n, n \geq 2 : r \leq |x| \leq R$} a special type of Trudinger-Moser-like inequality holds. Next we show how to infer from it a lack of blowup of radially symmetric solutions to a Keller-Segel system in $\Omega$.
Citation: Tomasz Cieślak. Trudinger-Moser type inequality for radially symmetric functions in a ring and applications to Keller-Segel in a ring. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2505-2512. doi: 10.3934/dcdsb.2013.18.2505
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