Sobolev Spaces in Higher Dimensions

Related lectures (31)

Page 3 of 4

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

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

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.

Covers the definition and properties of Hilbert spaces, including the Cauchy-Schwarz inequality and norm definition.

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

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.