Interplay of Sobolev Spaces on Compact Manifolds: Embedding Theorems, Inequalities, and Compactness
Interplay of Sobolev Spaces on Compact Manifolds: Embedding Theorems, Inequalities, and Compactness
This research paper explores various properties of Sobolev spaces on compact manifolds, focusing on embedding theorems, compactness, and inequalities. We establish the compact embedding of Sobolev spaces into continuous and Lebesgue spaces, as well as the continuity and compactness of embeddings between different Sobolev spaces. We also derive inequalities involving …