Lectures related to Regularity of Weak Solutions

Construction of Solutions by Dirichlet-Laplace

Explores the construction of solutions by Dirichlet-Laplace in general domains.

Geodesic Curves: Minimizing Distance and Constant Speed

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

General Existence Results for PDEs

Covers the general existence result for the Laplace-Dirichlet problem and the properties of the Newtonian potential.

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Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Analysis IV: Convergence Theorems and Integrable Functions

Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.

Elliptic Partial Differential Equations

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.