Regularity in Higher Dimension

Related lectures (29)

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Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

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

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Covers the study of translation groups on the interval [0,1] with different phases and the Riesz representation theorem on Hilbert space.

Covers internal heat transfer effects in heterogeneous reactions, emphasizing dimensionless numbers and transport effects.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

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