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Uniform a priori estimates for critical order Lane-Emden system in arbitrary dimensions | | Wei Dai
; Leyun Wu
; | | Date: |
1 Aug 2022 | | Abstract: | In this paper, we establish uniform a priori estimates for positive solutions
to the higher critical order superlinear Lane-Emden system in bounded domains
with Navier boundary conditions in arbitrary dimensions. First, we prove the
monotonicity of solutions for odd order (higher order fractional system) and
even order system (higher integer order system) respectively along the inward
normal direction near the boundary by the method of moving planes in local
ways. Then we derive uniform a priori estimates by establishing the
relationships between the maxima of $u$, $v$, $-Delta u$ and $-Delta v$
through Harnack inequality. In particular, we prove in Lemma 4.3 that if one of
$(u,v)$ is uniformly bounded then the other is also uniformly bounded. With
such a priori estimates, one will be able to obtain the existence of solutions
via topological degree theory or continuation argument. | | Source: | arXiv, 2208.00645 | | Services: | Forum | Review | PDF | Favorites | |
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