Lectures related to Optimal Transport: Analysis and Proofs

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

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

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.

Sub/Super Harmonic Functions

Explores sub/super harmonic functions and their applications in a theoretical context.

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Hadamard Factorisation

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Extreme Points and Compact Intervals

Covers extreme points, compact intervals, and optimization problems in analysis.

Distribution & Interpolation Spaces

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

Construction of Measures: Separation and Partition

Covers the construction of measures in RN, focusing on separation and partition of compact sets.

Linear Independence: The Wronskian Concept

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

Limits of Functions in Several Variables

Explores limits of functions in several real variables, including the two gendarmes theorem and the minimum and maximum theorem on compact sets.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Linear Independence: The Wronskian Concept

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