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pro vyhledávání: '"Zhang, Chilin"'
We establish an area growth estimate for solutions that are bounded from above of the Liouville equation $\Delta u+K e^{2u}=0$ with a positive pinched curvature $0<\lambda\leq K\leq\Lambda$. As an application, we provide a new proof of Eremenko-Gui-L
Externí odkaz:
http://arxiv.org/abs/2409.19327
Autor:
Zhang, Chilin
In this thesis, we study minimizers of the energy functional 𝐽 (𝑢,Ω) = ∫_Ω |∇𝑢|²/2 + 𝑊(𝑢) 𝑑𝑥 for two different potentials 𝑊(𝑢). In the first part we consider the Allen-Cahn energy, where 𝑊(𝑢) = (1 − 𝑢²)²
Autor:
Huang, Yupei, Zhang, Chilin
In \cite{elgindi2022regular}, a family of singular steady states near the Bahouri-Chemin patch was introduced. In this paper, we obtain the optimal regularity and convergence of the singular steady states contruced in \cite{elgindi2022regular} to the
Externí odkaz:
http://arxiv.org/abs/2311.11112
Autor:
Zhang, Chilin
We prove the $C^{2,\alpha}$ regularity of the free boundary in the Signorini problem with variable coefficients. We use a $C^{1,\alpha}$ boundary Harnack inequality in slit domain. The key method is to study a non-standard degenerate elliptic equatio
Externí odkaz:
http://arxiv.org/abs/2307.12466
Autor:
Zhang, Chilin
Publikováno v:
Nonlinear Anal. 240 (2024), Paper No. 113471, 16 pp
We establish a C^1,alpha Schauder estimate of a non-standard degenerate elliptic equation and use it to give another proof of the higher order boundary Harnack inequality. As an application, we obtain the analyticity of the free boundary in the class
Externí odkaz:
http://arxiv.org/abs/2303.04182
Autor:
Zhang, Chilin
Publikováno v:
In Nonlinear Analysis March 2024 240