Lecture

Regularity in Higher Dimension

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MATH-437: Calculus of variations

Introduction to classical Calculus of Variations and a selection of modern techniques. The Calculus of Variations aims at showing the existence of minimisers (or critical points) of functionals that naturally appear in mathematics and physics (Dirichlet en ...

Description

This lecture covers the concept of regularity in higher dimensions for scalar problems, focusing on the minimizer which solves the problem. It discusses the weak sense of the solution and the interior regularity up to the boundary. The lecture also explores the general approach and the partition of unity in the context of higher-dimensional problems.

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