Sobolev Spaces and Continuous Embeddings

Related lectures (30)

Page 1 of 3

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Explores real functions, covering parity, periodicity, and polynomial functions.

Explores embedding theorems in Sobolev spaces, including continuous and compact embedding, weak convergence, and Poincaré inequality.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Covers functions, including even and odd functions, periodicity, and function operations.