Let $(\tau_h)$ be a shape regular triangulation. Prove that there exists a constant $c>0$ such that $$\|v\|_{H^1(\Omega)}\leq \frac{c}{\min_{T\in\tau_h}} \|v\|_{L^2(\Omega)}$$ for all $v\in V^h$ where $V^h$ is a finite element space.
I know that I have to show the estimate $\|v\|_{H^1(T)}\leq c \|v\|_{L^2(T)}$ where $T$ is the reference triangle. By transformation we obtain the above inequality.
But I don't know how to prove the estimate on the triangle.