General Existence Results for PDEs

Related lectures (30)

Page 2 of 3

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Explains harmonic functions and their boundary conditions, including Dirichlet and Robin conditions.

Discusses the uniqueness of solutions for the Poisson equation and introduces the concept of Green function.

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

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

Explores the composition of applications in mathematics and the importance of understanding their properties.

Explores the Laplace equation, harmonic potential, and boundary conditions in groundwater flow, with practical examples.