Optimal Transport: Analysis and Proofs

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Theorems in Analysis

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

Harmonic Forms: Main Theorem

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

Initial Problem Solutions

Covers the description of problem solutions and the concept of compactness and uniform continuity.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Limits of Multivariable Functions: Techniques and Theorems

Discusses limits of multivariable functions, focusing on definitions, examples, and techniques for calculating limits effectively.

Compact Sets and Extreme Values

Explores compact sets, extreme values, and function theorems on bounded sets.

Differentiating under the integral sign

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

Maximum and Minimum of Functions

Explores limits, minimum and maximum values of functions, and continuity criteria in a compact set.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.