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Singularity estimates for elliptic systems of $m$-Laplacians
Yayun Li,Bei Liu 대한수학회 2018 대한수학회지 Vol.55 No.6
This paper is concerned about several quasilinear elliptic systems with $m$-Laplacians. According to the Liouville theorems of those systems on $\mathbb R^n$, we obtain the singularity estimates of the positive $C^1$-weak solutions on bounded or unbounded domain (but it is not $\mathbb R^n$) and their decay rates on the exterior domain when $|x| \to \infty$. The doubling lemma which is developed by Polacik-Quittner-Souplet plays a key role in this paper. In addition, the corresponding results of several special examples are presented.
SINGULARITY ESTIMATES FOR ELLIPTIC SYSTEMS OF m-LAPLACIANS
Li, Yayun,Liu, Bei Korean Mathematical Society 2018 대한수학회지 Vol.55 No.6
This paper is concerned about several quasilinear elliptic systems with m-Laplacians. According to the Liouville theorems of those systems on ${\mathbb{R}}^n$, we obtain the singularity estimates of the positive $C^1$-weak solutions on bounded or unbounded domain (but it is not ${\mathbb{R}}^n$ and their decay rates on the exterior domain when ${\mid}x{\mid}{\rightarrow}{\infty}$. The doubling lemma which is developed by Polacik-Quittner-Souplet plays a key role in this paper. In addition, the corresponding results of several special examples are presented.
Yi Yang,Min Li,Aijun Tang,Yayun Liu,Zhen Li,Shaohai Fu 한국섬유공학회 2020 Fibers and polymers Vol.21 No.8
Conventional colored latex particles have poor solvent resistance due to the absence of chemical bonds betweenthe dye and polymer component, resulting in staining and greatly restricting its application. In this research, the disperse dyewas chemically bonded to the polymer to prepare covalent and solvent-resistance colored latex particles. Firstly, C.I. DisperseRed 60, as a common disperse dye in industry, was modified by acryloyl chloride (amidation reaction) for the purpose ofintroducing the C=C bonds. The structure of modified C.I. Disperse Red 60 was confirmed by 1HNMR, FTIR and elementalanalysis and its spectral property was also evaluated. Then the covalent colored latex particles were synthesized via miniemulsioncopolymerization of styrene (St) and ethyl acrylate (EA) in presence of modified C.I. Disperse Red 60 monomer. Results of FTIR, TG, DSC and TEM indicated that the covalent colored latex particles were successfully prepared. By usingUV-spectroscopy, the solvent resistance of the colored latex membranes in petroleum ether, hexane, cyclohexane, and ethanolwas monitored, respectively. Slight change of the absorption was detected for 10 days, which verified the excellent solventresistance of covalent colored latex membranes. Finally, the prepared colored latex particles were applied on cotton printingin the absence of binder. The results showed that the colored latex particles printed fabric had superior rubbing fastness andsoft hand feel.