Maximum and Minimum Values: Theorems and Continuity

Related lectures (31)

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

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Covers the concept of uniform continuity and a theorem on continuous functions.

Discusses the Extreme Values Theorem for continuous functions on closed intervals.

Explores the chain rule for compositions of differential functions in higher dimensions, emphasizing gradients and directional changes.

Explores the necessity of uniform continuity for continuous functions on compact sets.

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Explores infimum, supremum, and absolute value concepts with examples and proofs.

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

Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.