Fundamental Solutions of Laplace Equation

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Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Explores uniqueness results for the Poisson equation and harmonic functions with different boundary conditions.

Covers the theory and applications of Green's function in solving differential equations.

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

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

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

Covers the Dirichlet problem on the ball and the solution to the Dirichlet problem on the half plane.

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

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