Sobolev embeddings

Jan Kalis

Florida Atlantic University

We prove a sharp Sobolev embedding with a zero boundary condition on a metric space which generalizes the real-case embedding. Using this new technique, we are able to prove a new sharp embedding on Lipschitz domains of $\mathbb{R}^{n}$ without the boundary condition. We also find the best constant for the real-case embedding and prove that this constant is not attained.