Delaunay-type singular solutions for the fractional Yamabe problem
We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity ( - Δ ) γ w = c n , γ w n + 2 γ n - 2 γ , w > 0 in R n \ { 0 } . We follow a variational approach, in which the key is the computation of the fractional Laplacian in polar coordinates.
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| Published in: | Mathematische annalen Vol. 369; no. 1-2; pp. 597 - 626 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01-10-2017
Springer Nature B.V |
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| Abstract | We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity
(
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Δ
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=
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+
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0
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\
{
0
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.
We follow a variational approach, in which the key is the computation of the fractional Laplacian in polar coordinates. |
|---|---|
| AbstractList | We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity
(
-
Δ
)
γ
w
=
c
n
,
γ
w
n
+
2
γ
n
-
2
γ
,
w
>
0
in
R
n
\
{
0
}
.
We follow a variational approach, in which the key is the computation of the fractional Laplacian in polar coordinates. We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity ( - Δ ) γ w = c n , γ w n + 2 γ n - 2 γ , w > 0 in R n \ { 0 } . We follow a variational approach, in which the key is the computation of the fractional Laplacian in polar coordinates. |
| Author | DelaTorre, Azahara del Pino, Manuel Wei, Juncheng González, María del Mar |
| Author_xml | – sequence: 1 givenname: Azahara surname: DelaTorre fullname: DelaTorre, Azahara organization: Universitat Politècnica de Catalunya – sequence: 2 givenname: Manuel surname: del Pino fullname: del Pino, Manuel organization: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile – sequence: 3 givenname: María del Mar orcidid: 0000-0001-8237-7642 surname: González fullname: González, María del Mar email: mar.gonzalez@upc.edu organization: Universitat Politècnica de Catalunya – sequence: 4 givenname: Juncheng surname: Wei fullname: Wei, Juncheng organization: Department of Mathematics, University of British Columbia |
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| Cites_doi | 10.3934/dcds.2013.33.2319 10.1016/j.jde.2012.03.024 10.1007/978-3-662-11761-3 10.4310/CAG.2001.v9.n1.a6 10.1093/oso/9780198505730.002.0002 10.1002/cpa.20153 10.1215/S0012-7094-99-09913-1 10.1512/iumj.2006.55.2706 10.1002/cpa.21564 10.1002/cpa.20116 10.1080/03605308208820218 10.12775/TMNA.1995.042 10.1016/j.bulsci.2011.12.004 10.1007/s00205-014-0722-4 10.1016/j.na.2015.10.009 10.1007/978-3-642-65183-0 10.1016/j.aim.2010.07.016 10.1007/BFb0089180 10.4171/JEMS/6 10.1007/s00032-013-0199-x 10.2140/apde.2013.6.1535 10.1002/cpa.20331 10.1080/03605300600987306 10.4171/JEMS/456 10.1007/s00526-008-0173-6 10.1016/j.jmaa.2014.04.048 |
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| Snippet | We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity
(
-
Δ
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γ
w
=
c
n
,
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w
n
+
2
γ
n
-
2
γ
,
w
>
0
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R
n
\
{... We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity ( - Δ ) γ w = c n , γ w n + 2 γ n - 2 γ , w > 0 in R n \ {... |
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| Title | Delaunay-type singular solutions for the fractional Yamabe problem |
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