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Last updated on October 25, 2017

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Topics in PDEs - Summer 2013

**Schedule of presentation **

- Tuesday, June 25: Harnack's principle (Section 8.3 of Lecture Notes) :: Anoushe
- Tuesday July 2:
- The Cauchy-Kovalevskaya Theorem, I: real analytic functions and statement of the theorem (Sections 2.2.1 and 2.23 of Renardy and Rogers) :: Zhe
- The Cauchy-Kovalevskaya Theorem, II: idea of the proof (Sections 2.23 and 2.2.4 of Renardy and Rogers) :: Jiteng
- A PDE without solutions (Thm. 2.25 in Section 2.2.5, Renardy and Rogers) :: Fatemeh
- Every distribution is a derivative of a continuous function (Theorem 6.26, p. 152 of Rudin's Functional Analysis) :: Dharmpreet
- Direct product of distributions (Vladimirov, "Methods of the Theory of Generalized Functions", Sections 3.1 - 3.3.) :: Mingcong

- Thursday July 4:
- Paley-Wiener Theorem (Section 14 of Lecture Notes) :: Subhajyoti
- Fundamental solution for the wave equation (various sources) :: Naghmeh
- Fourier series (various sources) :: Abdullah
- Structure theorem for tempered distributions (Vladimirov, "Methods of the Theory of Generalized Functions", Section 5.4.) :: Friday
- Proof of the Malgrange-Ehrenpreis Theorem :: Josue