Fix inline math in linear-elasticity-intro.md

Make sure that all inline math can be displayed correctly in the GitHub preview for markdown files.

Author: yguclu

chapter2/linear-elasticity-intro.md

@@ -1,7 +1,7 @@
 # Linear Elasticity
 
 ## The PDE problem
-The governing equations for small elastic deformations of a body $ \Omega $ can be expressed as:
+The governing equations for small elastic deformations of a body $\Omega$ can be expressed as:
 
 $$
 \begin{align}
@@ -10,18 +10,18 @@ $$
 \end{align}
 $$
 
-where $ \sigma $ is the stress tensor, $ f $ represents the body force per unit volume, $ \kappa $ and $ \mu $ are Lamé's elasticity parameters for the material, $ I $ denotes the identity tensor, $ \epsilon $ is the symmetric strain tensor and the displacement vector field is denoted by $ u $. $ \epsilon := \frac{1}{2}(\nabla u + (\nabla u)^T) $
+where $\sigma$ is the stress tensor, $f$ represents the body force per unit volume, $\kappa$ and $\mu$ are Lamé's elasticity parameters for the material, $I$ denotes the identity tensor, $\epsilon$ is the symmetric strain tensor and the displacement vector field is denoted by $u$. $\epsilon := \frac{1}{2}(\nabla u + (\nabla u)^T)$
 
 
 
-By substituting $ \epsilon(u) $ into $ \sigma $, we obtain:
+By substituting $\epsilon(u)$ into $\sigma$, we obtain:
 
 $$
 \sigma(u) = \kappa (\nabla \cdot u)I + \mu(\nabla u + (\nabla u)^T)
 $$
 
 Then, the strong formulation of linear elasticity is :
-Find $ u \in V $ such that
+Find $u \in V$ such that
 
 $$
 \begin{align}
@@ -32,12 +32,12 @@ $$
 $$
 
 where : 
-- $ V = \{ v \in (H^1(\Omega))^3 : v = 0 \text{ on } \partial \Omega_D \} $,
+- $V = \{ v \in (H^1(\Omega))^3 : v = 0 \text{ on } \partial \Omega_D \}$,
 
-- $ g_D $ is the Dirichlet boundary condition on the part $ \partial \Omega_D $ of the boundary,
+- $g_D$ is the Dirichlet boundary condition on the part $\partial \Omega_D$ of the boundary,
 
-- $ g_T $ is the traction vector on the part $ \partial \Omega_T $ of the boundary,
+- $g_T$ is the traction vector on the part $\partial \Omega_T$ of the boundary,
 
-- $ n $ is the outward normal vector on the boundary $ \partial \Omega $,
+- $n$ is the outward normal vector on the boundary $\partial \Omega$,
 
-- $ \partial \Omega_D \cap \partial \Omega_T = \emptyset $ and $ \partial \Omega = \partial \Omega_D \cup \partial \Omega_T $.
+- $\partial \Omega_D \cap \partial \Omega_T = \emptyset$ and $\partial \Omega = \partial \Omega_D \cup \partial \Omega_T$.