Geodesic
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures
Mathematica Bohemica, Tome 146 (2021) no. 3, pp. 235-249 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $u^{\#}$.
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 $u^{\#}$.
DOI : 10.21136/MB.2020.0165-18
Classification : 35J25, 35J61, 35R06
Keywords: elliptic equation; exponential nonlinearity; scalar Chern-Simons equation; signed measure 
@article{10_21136_MB_2020_0165_18,
     author = {Presoto, Adilson Eduardo},
     title = {The non-uniqueness of the limit solutions of the scalar {Chern-Simons} equations with signed measures},
     journal = {Mathematica Bohemica},
     pages = {235--249},
     year = {2021},
     volume = {146},
     number = {3},
     doi = {10.21136/MB.2020.0165-18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0165-18/}
}
TY  - JOUR
AU  - Presoto, Adilson Eduardo
TI  - The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures
JO  - Mathematica Bohemica
PY  - 2021
SP  - 235
EP  - 249
VL  - 146
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0165-18/
DO  - 10.21136/MB.2020.0165-18
LA  - en
ID  - 10_21136_MB_2020_0165_18
ER  - 
%0 Journal Article
%A Presoto, Adilson Eduardo
%T The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures
%J Mathematica Bohemica
%D 2021
%P 235-249
%V 146
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0165-18/
%R 10.21136/MB.2020.0165-18
%G en
%F 10_21136_MB_2020_0165_18
Presoto, Adilson Eduardo. The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures. Mathematica Bohemica, Tome 146 (2021) no. 3, pp. 235-249. doi: 10.21136/MB.2020.0165-18

Cité par Sources :