Embedding of $W^{1,2}(\mathbb{R^2})$ in $L^p(\mathbb{R^2})$ for all $2\leq p<\infty$

Question

I need to prove the above embeddeding. Here as $p=n$ as we are working in $\mathbb{R^2}$ so we can't apply the sobolev embedding also the domain is not bounded. Any idea regarding how to approach this would be beneficial.