| Date | Teacher | Place | Topic | Lecture notes / comments |
| 24.08.2010 | Ujjwal Koley? | B71? | Introduction? | Some repetition (?); Integration by part in R^n and formulas which follow from it; Multidimensional chain rule; Convolution; Laplace equation? |
| 27.08.2010 | Ujjwal Koley? | B70? | Laplace equation? | Poisson's equation; Harmonic functions, Fundamental solution.? |
| 31.08.2010 | Ujjwal Koley? | B71? | Mean Value theorem? | Mean-value formulas; Maximum principle ? |
| 03.09.2010 | Ujjwal Koley? | B70? | Regularity? | Regularity theorem, Liouville's theorem, Harnack's inequality, Introduction to Green's function? |
| 07.09.2010 | Nils Henrik Risebro? | B71? | Green's functions? | Symmetry of the Green's function. Green's function for a half plane and a sphere.? |
| 10.09.2010 | NIls Henrik Risebro? | B70? | Green's functions, energy methods? | The students show that the formula for the sphere is correct. I give some energy arguments.? |
| 14.09.2010 | Achenef Tesfahun? | B71? | H?lder spaces. Mollifiers? | H?lder spaces. Mollifiers; smooth approximation of locally integrable functions? |
| 17.09.2010 | Achenef Tesfahun? | B70? | Weak derivatives, Sobolev spaces? | Weak derivatives and Sobolev spaces: L.C. Evans Page 242-245. Fundamental Theorem of calculus of Variation. ? |
| 21.09.2010 | Achenef Tesfahun? | B71? | Sobolev spaces? | Example, properties of weak derivatives and Sobolev spaces, Sobolev spaces as function spaces: L.C. Evans, page 246-249.? |
| 24.09.2010 | Achenef Tesfahun? | B70? | Exercises? | We will do the exercises (2.5.2-2.5.8 ) in L. C. Evans, page 85-87.? |
| 28.09.2010 | Achenef Tesfahun? | B71? | Sobolev spaces, approximation? | Approximating a function in Sobolev spaces by smooth functions. L. C. Evans page 250-254? |
| 01.10.2010 | Achenef Tesfahun? | B70? | Sobolev spaces: Extension, Traces? | Extension and Trace Theorems for Sobolev spaces. L. C. Evans page 254-259? |
| 05.10.2010 | Achenef Tesfahun? | B71? | Sobolev spaces: Traces, Sobolev inequalities? | We continue on the proof of Trace Theorem. I will also give the proof for Gagliardo-Nirenberg-Sobolev inequality. L.C.Evans page 258-264? |
| 08.10.2010 | Achenef Tesfahun? | B70? | Sobolev Spaces: Sobolev inequalities? | Estimates in W^{1,p} and W_0^{1,p} (when p<n). We will also see Morrey's inequality (when n<p). L.C. Evans (page 265-269)? |
| 12.10.2010 | Achenef Tesfahun? | B71? | Sobolev Spaces: Sobolev inequalities? | We finish proof of Morrey's inequalities, and see Theorem 5 (page 269 of the book). We will also do the proofs for the general Sobolev inequalities (page 270-271 of the book).? |
| 15.10.2010 | Achenef Tesfahun? | B70? | Exercises? | We will do the exercises 3, 5, 6, 7, 8 and 13 (if we get time) in L. C. Evans, page 290-291.? |
| 19.10.2010 | Xavier Raynaud? | B71? | Compactness. Arzela-Ascoli and Rellich-Kondrachov theorems? | section 5.7? |
| 22.10.2010 | --? | B70? | Rellich-Kondrachov theorem - Poincare inequality? | sections 5.7, 5.8.1. NB: lecture finishes at 13:15.? |
| 26.10.2010 | --? | B71? | Fourier transform? | Exercises 5.10.10, 5.10.14section 4.3.1? |
| 29.10.2010 | --? | B70? | Fourier transform - H^s spaces? | Section 5.8.4. Appendix D.Exercise on Fourier transform of a Gaussian . Exercises 5.10.15? |
| 02.10.2010 | --? | B71? | Some results and definitions from linear functional analysis? | Some parts of appendix D Riesz representation theoremElliptic equation (intro)? |
| 05.10.2010 | --? | B70? | Weak solutions to elliptic equations and Lax-Milgram theorem? | Exercise on weak convergence . Exercise 5.10.18? |
| 09.11.2010 | --? | B71? | Existence of weak solutions - Regularity theory? | ? |
| 12.11.2010 | --? | B70? | Regularity theory - Difference quotient? | Exercise on Poincare's inequalityOppgave 1 and 2 from (i) to (v) in exam 2008? |
| 16.11.2010 | --? | B71? | Interior regularity? | ? |
| 17.11.2010 | --? | B70? | Boundary regularity? | Exercise on higher interior regularityProblem 1 in exam 2009Oppgave 1 in exam 2005? |
| 23.11.2010 | --? | B71? | Maximum principle? | ? |
| 26.11.2010 | --? | B70? | Maximum principle? | Exercise on regularityEnd of oppgave 2 in exam 2008? |
| 30.11.2010 | --? | B71? | Maximum principle - Weak solution (rep.)? | ? |
| 03.12.2010 | --? | B70? | ? | Exercise 6.6.2Problem 2 and 3 in exam 2009Problem 1 in exam 2006 There is an error in that problem. We will just shortly discuss it.Problem 2 in exam 2004? |
Teaching plan
Published July 5, 2010 10:33 AM
- Last modified Dec. 2, 2010 5:35 PM