| Title:
|
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures (English) |
| Author:
|
Presoto, Adilson Eduardo |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
235-249 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the effect of admitting signed measures as a datum at the scalar Chern-Simons equation \[ -\Delta u + {\rm e}^u({\rm e}^u-1) =\mu \quad \mbox {in}\ \Omega \] with the Dirichlet boundary condition. Approximating $\mu $ by a sequence $(\mu _n)_{n \in \mathbb N}$ of $L^1$ functions or finite signed measures such that this equation has a solution $u_n$ for each $n\in \mathbb {N}$, we are interested in establishing the convergence of the sequence $(u_n)_{n\in \mathbb {N}}$ to a function $u^{\#}$ and describing the form of the measure which appears on the right-hand side of the scalar Chern-Simons equation solved by $u^{\#}$. (English) |
| Keyword:
|
elliptic equation |
| Keyword:
|
exponential nonlinearity |
| Keyword:
|
scalar Chern-Simons equation |
| Keyword:
|
signed measure |
| MSC:
|
35J25 |
| MSC:
|
35J61 |
| MSC:
|
35R06 |
| DOI:
|
10.21136/MB.2020.0165-18 |
| . |
| Date available:
|
2021-08-18T08:21:00Z |
| Last updated:
|
2021-08-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149066 |
| . |
| 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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| Reference:
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