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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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2021-10-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/146/3/mb146_3_1.pdf |
| 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\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 $u^#$. |
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| ISSN: | 0862-7959 2464-7136 |