如何在 LaTeX 中书​​写长方程式？

Question

我正在尝试正确、系统地写出这个数学表达式。我需要一些帮助，请：

\begin{equation} \label{58}
\begin{array}{l}
\alpha_{\mathcal{A}}\|w_n-w_n^{hk}\|^2_V \\
&\leq \langle \mathcal{A}\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),\varepsilon(w_n-v_n^h) \rangle_{\mathcal{H}}+ \langle\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} +\langle F_n,w_n-v_n^h\rangle_V\\
&+ \langle\mathcal{B}^l(\varepsilon(u_n)),\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h -w_n^{hk})\rangle_{\mathcal{H}} +\langle\int_{0}^t \mathcal{G}^l(t-s)u_n \mathrm{d}s,\varepsilon(w_n^{hk}-
w_n)\rangle_{\mathcal{H}}  \\

& + \langle\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk}\mathrm{d}s,\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} +
\langle(\mathcal{P^*})^l\nabla \varphi_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}}  \\

&-\langle \mathcal{C}^l\theta_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}- \langle \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} +
 \int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \mathrm{d}a  \\  
 
&+\int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \mathrm{d}s  \\
&\leq \langle \mathcal{A}^l\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),\varepsilon(w_n-v_n^h) \rangle_{\mathcal{H}}   +\langle\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} + \langle\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} \\

&+ \langle\mathcal{B}^l(\varepsilon(u_n)) -\mathcal{B}^l(\varepsilon(u_n^{hk}))  ,\varepsilon(w_n^{hk} -w_n)\rangle_{\mathcal{H}} +\langle\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk} \mathrm{d}s,\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} \\

&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n \mathrm{d}s-\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk} \mathrm{d}s,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}+ \langle(\mathcal{P^*})^l\nabla \varphi_n -( \mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}\\

&+ \langle(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} - \langle \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} -\langle \mathcal{C}^l\theta_n- \mathcal{C}^l\theta_n^{hk},\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} \\

&+ \langle F_n,w_n-v_n^h\rangle_V + 
\int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \mathrm{d}a \\

&+\int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \mathrm{d}a \\

&+
\int_{\Gamma_3} j_{\nu}^0(w_{n\nu}^{hk};v_n^h-w_n) \mathrm{d}a + j_\tau^0(w_{n\tau}^{hk};v_n^h-w_{n\nu}) \mathrm{d}a
\end{array}
\end{equation}

Answer 1

的一个变体array。但请注意\innpr，特别是在积分附近。

\documentclass{article}
\usepackage{amsmath, amssymb,array,mathtools}

\DeclarePairedDelimiter{\innpr}{\langle}{\rangle}

\begin{document}

\begin{equation} \label{eq:58}
\setlength{\arraycolsep}{0pt}
\renewcommand{\arraystretch}{2}
\begin{array}{
  l<{\vphantom{\displaystyle\int_0^t}}
  >{\quad{}}r<{{}}
  >{\quad{}}r<{{}}
  >{\displaystyle}l
}
\multicolumn{4}{l}{\displaystyle\alpha_{\mathcal{A}}\|w_n-w_n^{hk}\|^2_V} \\
&\leq&
  \multicolumn{2}{l}{\displaystyle
    \innpr{ \mathcal{A}\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),
    \varepsilon(w_n-v_n^h) }_{\mathcal{H}}
    +\innpr{\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)}_{\mathcal{H}}}
\\
&&+& \innpr{ F_n,w_n-v_n^h}_V \\
&&+& \innpr{\mathcal{B}^l(\varepsilon(u_n)),\varepsilon(w_n^{hk}-w_n)}_{\mathcal{H}} + \innpr{\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h -w_n^{hk})}_{\mathcal{H}} \\
&&+& \innpr[\Big]{\int_{0}^t \mathcal{G}^l(t-s)u_n \, ds,\varepsilon(w_n^{hk}-w_n)}_{\mathcal{H}} \\
&&+& \innpr[\Big]{\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk}\, ds,\varepsilon(v_n^h-w_n^{hk})}_{\mathcal{H}} \\
&&+& \innpr{(\mathcal{P^*})^l\nabla \varphi_n,\varepsilon(w_n^{hk}-w_n)}_{\mathcal{H}} + \innpr{(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n^{hk})}_{\mathcal{H}} \\
&&-& \innpr{ \mathcal{C}^l\theta_n,\varepsilon(w_n^{hk}-w_n)}_{\mathcal{H}}- \innpr{ \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n^{hk})}_{\mathcal{H}} \\
&&+& \int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da  \\
&&+& \int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da \\
&&+& \int_{\Gamma_3} j_{\nu}^0(w_{n\nu}^{hk};v_n^h-w_n) \, da + j_\tau^0(w_{n\tau}^{hk};v_n^h-w_{n\nu}) \, da
\end{array}
\end{equation} 

\end{document}

\begin{array}[b]如果希望公式编号位于底部，请使用。

Answer 2

@Sebastiano 回答后的一些建议：

a) 我更喜欢等距的线条。实现此目的的一种（粗略）方法是\phantom{\int_0^t}在较短的线条中使用 a。

b) 我会大概最好将其\leq放在第一行，而不是第二行。

\documentclass{article}
\usepackage{amsmath, amssymb}

\begin{document}

\begin{equation} \label{eq:58}
\begin{split}
\alpha_{\mathcal{A}}&\|w_n-w_n^{hk}\|^2_V \leq\\
&  \langle \mathcal{A}\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),\varepsilon(w_n-v_n^h) \rangle_{\mathcal{H}}+ \langle\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}}  \phantom{\int_0^t} \\
&+ \langle F_n,w_n-v_n^h\rangle_V \phantom{\int_0^t}\\
&+ \langle\mathcal{B}^l(\varepsilon(u_n)),\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h -w_n^{hk})\rangle_{\mathcal{H}} \phantom{\int_0^t}\\
&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n \, ds,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} \\
&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk}\, ds,\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \\
&+ \langle(\mathcal{P^*})^l\nabla \varphi_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \phantom{\int_0^t}\\
&- \langle \mathcal{C}^l\theta_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}- \langle \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}}  \phantom{\int_0^t}\\
&+ \int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da  \\
&+ \int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da \\
&+ \int_{\Gamma_3} j_{\nu}^0(w_{n\nu}^{hk};v_n^h-w_n) \, da + j_\tau^0(w_{n\tau}^{hk};v_n^h-w_{n\nu}) \, da
\end{split}
\end{equation} 

\end{document}

Answer 3

使用split环境（参见@cabohah 的评论）。

\documentclass{article}
\usepackage{amsmath, amssymb}

\begin{document}

\begin{equation} \label{eq:58}
\begin{split}
&\alpha_{\mathcal{A}}\|w_n-w_n^{hk}\|^2_V \\
&\leq \langle \mathcal{A}\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),\varepsilon(w_n-v_n^h) \rangle_{\mathcal{H}}+ \langle\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} \\
&+ \langle F_n,w_n-v_n^h\rangle_V \\
&+ \langle\mathcal{B}^l(\varepsilon(u_n)),\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h -w_n^{hk})\rangle_{\mathcal{H}} \\
&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n \, ds,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} \\
&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk}\, ds,\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \\
&+ \langle(\mathcal{P^*})^l\nabla \varphi_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \\
&- \langle \mathcal{C}^l\theta_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}- \langle \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \\
&+ \int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da  \\
&+ \int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da \\
&+ \int_{\Gamma_3} j_{\nu}^0(w_{n\nu}^{hk};v_n^h-w_n) \, da + j_\tau^0(w_{n\tau}^{hk};v_n^h-w_{n\nu}) \, da
\end{split}
\end{equation} 

\end{document}