| Title:
|
Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential (English) |
| Author:
|
Žubrinić, Darko |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
429-435 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of $p$-Laplacian type. If $p<\gamma <N$ and the right-hand side is a Radon measure with singularity of order $\gamma $ at $x_0\in \Omega $, then any supersolution in $W_{\mathrm loc}^{1,p}(\Omega )$ has singularity of order at least $\frac{(\gamma -p)}{(p-1)}$ at $x_0$. In the proof we exploit a pointwise estimate of $\mathcal A$-superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure. (English) |
| Keyword:
|
quasilinear elliptic |
| Keyword:
|
singularity |
| Keyword:
|
Sobolev function |
| MSC:
|
31B05 |
| MSC:
|
35A20 |
| MSC:
|
35B05 |
| MSC:
|
35J60 |
| idZBL:
|
Zbl 1022.31005 |
| idMR:
|
MR1983463 |
| . |
| Date available:
|
2009-09-24T11:03:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127811 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| . |
