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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Main Author: Adilson Eduardo Presoto
Format: Article
Language:English
Published: Institute of Mathematics of the Czech Academy of Science 2021-10-01
Series:Mathematica Bohemica
Subjects:
Online Access:http://mb.math.cas.cz/full/146/3/mb146_3_1.pdf
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spelling 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
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