"리우빌 방정식"의 두 판 사이의 차이

2015년 11월 7일 (토) 07:30 판

$$\Delta \phi =-2 K e^{\phi }$$ 여기서 $\Delta$는 라플라시안(Laplacian)

$$ g(x,y)(dx^2+dy^2),\,g(x,y)=e^{\phi(x,y)} $$

$$ K=-\frac{1}{2}e^{-\phi (x,y)}\left(\frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2}\right) $$

$$ e^{\phi}=\frac{|f'(z)|^2}{(\Im f(z))^2} $$

Part 1 | Introduction to Conformal Field Theory: Liouville Model | Leon Takhtajan , 2013. https://www.youtube.com/watch?v=-O555nA-hrg.

Levi, D., L. Martina, and P. Winternitz. ‘Structure Preserving Discretizations of the Liouville Equation and Their Numerical Tests’. arXiv:1504.01953 [math-Ph, Physics:nlin], 8 April 2015. http://arxiv.org/abs/1504.01953.
Huang, Ying. ‘New No-Traveling Wave Solutions for the Liouville Equation by Bäcklund Transformation Method’. Nonlinear Dynamics 72, no. 1–2 (4 December 2012): 87–90. doi:10.1007/s11071-012-0692-8.
Brito, Francisco, Maria Luiza Leite, and Vicente De Souza Neto. Liouville’s Formula Under the Viewpoint of Minimal Surfaces, n.d. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.360.4767
Brito, Francisco, and Maria Luiza Leite. ‘Uniqueness and Globality of the Liouville Formula for Entire Solutions of $ {\partial^{2}\log \lambda \over \partial Z \partial \overline Z} + {\lambda \over 2} = 0 $’. Archiv Der Mathematik 80, no. 5 (1 May 2003): 501–6. doi:10.1007/s00013-003-0481-1.

@@ 21번째 줄: / 21번째 줄: @@
 ==메모==
 * http://benasque.org/2009gph/talks_contr/105Pablo-Mira.pdf
-* $\pi_{z\bar{z}}=\frac{1}{2}e^{\phi}$
+* $\phi_{z\bar{z}}=\frac{1}{2}e^{\phi}$
+* 리우빌 해, 해석함수 $f$에 대하여, 아래의 $\phi$는 리우빌 방정식의 해이다
+$$
+e^{\phi}=\frac{|f'(z)|^2}{(\Im f(z))^2}
+$$
 ==관련된 항목들==