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In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation
FREE
This course includes
Hours of videos
638 years, 9 months
Units & Quizzes
23
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates
Course Currilcum
- Review of Harmonic Functions and the Perspective We Take on Elliptic PDE Unlimited
- Finding Other Second Derivatives from the Laplacian Unlimited
- Korn’s Inequality I Unlimited
- Korn’s Inequality II Unlimited
- Schauder’s Inequality Unlimited
- Using Functional Analysis to Solve Elliptic PDE Unlimited
- Sobolev Inequality I Unlimited
- Sobolev Inequality II Unlimited
- De Giorgi-Nash-Moser Inequality Unlimited
- Nonlinear Elliptic PDE I Unlimited
- Nonlinear Elliptic PDE II Unlimited
- Barriers Unlimited
- Minimal Graphs Unlimited
- Gauss Circle Problem I Unlimited
- Gauss Circle Problem II Unlimited
- Fourier Analysis in PDE and Interpolation Unlimited
- Applications of Interpolation Unlimited
- Calderon-Zygmund Inequality I Unlimited
- Calderon-Zygmund Inequality II Unlimited
- Littlewood-Paley Theory Unlimited
- Strichartz Inequality I Unlimited
- Strichartz Inequality II Unlimited
- The Nonlinear Schrödinger Equation Unlimited
