The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures
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\quadin \Omega with the Dirichlet boundary condition. Approximating $\mu$ by a sequence $(\mu_n)_{n \in\mathbb N}$ of $L^1$ functions or finite signed mea...
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Institute of Mathematics of the Czech Academy of Science
2021-10-01
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Online Access: | http://mb.math.cas.cz/full/146/3/mb146_3_1.pdf |
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doaj-04320ed2f353470f8aac5e7a0695e0d82021-08-13T05:11:40ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362021-10-01146323524910.21136/MB.2020.0165-18MB.2020.0165-18The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measuresAdilson Eduardo PresotoWe 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\quadin \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 $u^#$.http://mb.math.cas.cz/full/146/3/mb146_3_1.pdf elliptic equation exponential nonlinearity scalar chern-simons equation signed measure |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Adilson Eduardo Presoto |
spellingShingle |
Adilson Eduardo Presoto The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures Mathematica Bohemica elliptic equation exponential nonlinearity scalar chern-simons equation signed measure |
author_facet |
Adilson Eduardo Presoto |
author_sort |
Adilson Eduardo Presoto |
title |
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures |
title_short |
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures |
title_full |
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures |
title_fullStr |
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures |
title_full_unstemmed |
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures |
title_sort |
non-uniqueness of the limit solutions of the scalar chern-simons equations with signed measures |
publisher |
Institute of Mathematics of the Czech Academy of Science |
series |
Mathematica Bohemica |
issn |
0862-7959 2464-7136 |
publishDate |
2021-10-01 |
description |
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\quadin \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 $u^#$. |
topic |
elliptic equation exponential nonlinearity scalar chern-simons equation signed measure |
url |
http://mb.math.cas.cz/full/146/3/mb146_3_1.pdf |
work_keys_str_mv |
AT adilsoneduardopresoto thenonuniquenessofthelimitsolutionsofthescalarchernsimonsequationswithsignedmeasures AT adilsoneduardopresoto nonuniquenessofthelimitsolutionsofthescalarchernsimonsequationswithsignedmeasures |
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1721209051099955200 |