Sub/Super Harmonic Functions

Related lectures (29)

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

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

Covers the approximation of functions in Sobolev spaces using smooth functions.

Covers the properties of harmonic functions and the concept of mollification.

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

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Explores differentiating under the integral sign and conditions for differentiation, with examples and extensions to functions on open intervals.

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.

Explores differentiating under the integral sign and continuity of functions in integrals.

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.