| Title:
|
A compactness result for polyharmonic maps in the critical dimension (English) |
| Author:
|
Zheng, Shenzhou |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
137-150 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For $n=2m\ge 4$, let $\Omega \in \mathbb {R}^n$ be a bounded smooth domain and ${\mathcal {N}\subset \mathbb {R}^L}$ a compact smooth Riemannian manifold without boundary. Suppose that $\{u_k\}\in W^{m,2}(\Omega ,\mathcal {N})$ is a sequence of weak solutions in the critical dimension to the perturbed $m$-polyharmonic maps $$\label {m-polyharmonic} \frac {\rm d}{{\rm d} t}\Big |_{t=0}E_m(\Pi (u+t\xi ))=0 $$ with $\Phi _k\rightarrow 0$ in $(W^{m,2}(\Omega ,\mathcal {N}))^*$ and $u_k\rightharpoonup u$ weakly in $W^{m,2}(\Omega ,\mathcal {N})$. Then $u$ is an $m$-polyharmonic map. In particular, the space of $m$-polyharmonic maps is sequentially compact for the weak-$W^{m,2}$ topology. (English) |
| Keyword:
|
polyharmonic map |
| Keyword:
|
compactness |
| Keyword:
|
Coulomb moving frame |
| Keyword:
|
Palais-Smale sequence |
| Keyword:
|
removable singularity |
| MSC:
|
35J35 |
| MSC:
|
35J48 |
| MSC:
|
58J05 |
| idZBL:
|
Zbl 06587880 |
| idMR:
|
MR3483229 |
| DOI:
|
10.1007/s10587-016-0246-1 |
| . |
| Date available:
|
2016-04-07T15:02:14Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144880 |
| . |
| Reference:
|
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