From 3a36ecb83b28ee504313b281400e96df2d5d2573 Mon Sep 17 00:00:00 2001 From: Silvio Fanzon Date: Mon, 12 Aug 2024 16:09:46 +0100 Subject: [PATCH] Signed-off-by: Silvio Fanzon --- _posts/2021-02-01-Calculus-of-Variations.md | 36 ++++++++++----------- 1 file changed, 18 insertions(+), 18 deletions(-) diff --git a/_posts/2021-02-01-Calculus-of-Variations.md b/_posts/2021-02-01-Calculus-of-Variations.md index 13c858e2ae2f..2c6bbbe00000 100644 --- a/_posts/2021-02-01-Calculus-of-Variations.md +++ b/_posts/2021-02-01-Calculus-of-Variations.md @@ -127,24 +127,24 @@ Lecture notes and video recordings of lectures are available at the links below -| **Date** | **Lecture Notes** | **Video Recordings** | **Topics** | -|: -------- |:------------- |:--------- |:--------- | -| 3 March | [Lesson 1](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_01.pdf) | [Part 1](https://youtu.be/2dMU_fnmbg4) | [Part 2](https://youtu.be/rjRNcZigdP0) | Introduction. Basic examples. Functional analysis revision | -| 10 March | [Lesson 2](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_02.pdf) | [Part 1](https://youtu.be/HXN3PbE0kD4) | [Part 2](https://youtu.be/1BHR3gfcPYI) | Functional Analysis Revision. Calculus in Normed Spaces | -| 17 March | [Lesson 3](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_03.pdf) | [Part 1](https://youtu.be/P8G2VTzdWw4), [Part 2](https://youtu.be/zeAfi3VjCGo) | Calculus in Normed Spaces. Indirect Method | -| 24 March | [Lesson 4](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_04.pdf) | [Part 1](https://youtu.be/eN3oi6vmaIg), [Part 2](https://youtu.be/KoT5sYjz0KE) | Fundamental Lemmas. Boundary conditions | -| 14 April | [Lesson 5](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_05.pdf) | [Part 1](https://youtu.be/-rN5lVqSNSo), [Part 2](https://youtu.be/m-fkISH4TJc) | Euler-Lagrange Equation | -| Extra | [Revision](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_05_revision.pdf) | [Video Overview](https://youtu.be/a9EB7gH__vI) | Revision of $$L^p$$ spaces | -| 21 April | [Lesson 6](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_06.pdf) | [Part 1](https://youtu.be/T9TrFIYlIW8), [Part 2](https://youtu.be/pown6pf4nGY) | Sufficient Conditions: convexity, trivial lemma. Convolutions| -| 28 April | [Lesson 7](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_07.pdf) | FLCV and DBR Lemma. Sobolev spaces | -| 5 May | [Lesson 8](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_08.pdf) | Sobolev Spaces: regularity and density results | -| 12 May | [Lesson 9](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_09.pdf) | Sobolev embedding. Ascoli-Arzelà | -| 19 May | [Lesson 10](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_10.pdf) | Higher order Sobolev Spaces. Traces. Euler-Lagrange Equation | -| 26 May | [Lesson 11](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_11.pdf) | Boundary conditions. Sufficient conditions. Direct Method | -| 2 June | [Lesson 12](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_12.pdf) | Direct method: example. General existence theorem | -| 9 June | [Lesson 13](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_13.pdf) | LSC Envelope. Relaxation and its computation | -| 16 June | [Lesson 14](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_14.pdf) | Relaxation of integral functionals. $$\Gamma$$-convergence | -| 23 June | [Lesson 15](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_15.pdf) | Examples of $$\Gamma$$-convergence. Homogenization problems | +| **Date** | **Lecture Notes** | **Video Recordings** | **Topics** | +|: -------- |:------------- |:--------- |:--------- | +| 3 March | [Lesson 1](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_01.pdf) | [Part 1](https://youtu.be/2dMU_fnmbg4)   |   [Part 2](https://youtu.be/rjRNcZigdP0) | Introduction. Basic examples. Functional analysis revision | +| 10 March | [Lesson 2](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_02.pdf) | [Part 1](https://youtu.be/HXN3PbE0kD4)   |   [Part 2](https://youtu.be/1BHR3gfcPYI) | Functional Analysis Revision. Calculus in Normed Spaces | +| 17 March | [Lesson 3](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_03.pdf) | [Part 1](https://youtu.be/P8G2VTzdWw4)   |   [Part 2](https://youtu.be/zeAfi3VjCGo) | Calculus in Normed Spaces. Indirect Method | +| 24 March | [Lesson 4](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_04.pdf) | [Part 1](https://youtu.be/eN3oi6vmaIg)   |   [Part 2](https://youtu.be/KoT5sYjz0KE) | Fundamental Lemmas. Boundary conditions | +| 14 April | [Lesson 5](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_05.pdf) | [Part 1](https://youtu.be/-rN5lVqSNSo)   |   [Part 2](https://youtu.be/m-fkISH4TJc) | Euler-Lagrange Equation | +| Extra | [Revision](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_05_revision.pdf) | [Video overview](https://youtu.be/a9EB7gH__vI) | Revision of $$L^p$$ spaces | +| 21 April | [Lesson 6](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_06.pdf) | [Part 1](https://youtu.be/T9TrFIYlIW8)   |   [Part 2](https://youtu.be/pown6pf4nGY) | Sufficient Conditions: convexity, trivial lemma. Convolutions| +| 28 April | [Lesson 7](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_07.pdf) | [Part 1](https://youtu.be/4weE16r31cc)   |   [Part 2](https://youtu.be/rOpTF0zuFP4) | FLCV and DBR Lemma. Sobolev spaces | +| 5 May | [Lesson 8](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_08.pdf) | [Part 1](https://youtu.be/38JAAgRrfOQ)   |   [Part 2](https://youtu.be/kssYL7cLQKU) | Sobolev Spaces: regularity and density results | +| 12 May | [Lesson 9](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_09.pdf) | [Part 1](https://youtu.be/PmWYyxGachg)   |   [Part 2](https://youtu.be/VyKQy9q_KyY) | Sobolev embedding. Ascoli-Arzelà Theorem | +| 19 May | [Lesson 10](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_10.pdf) | [Part 1](https://youtu.be/U-SaPTtzPnM)   |   [Part 2](https://youtu.be/VWHRA5LnXBk) | Higher order Sobolev Spaces. Traces. Euler-Lagrange Equation | +| 26 May | [Lesson 11](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_11.pdf) | [Part 1]()   |   [Part 2]() | Boundary conditions. Sufficient conditions. Direct Method | +| 2 June | [Lesson 12](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_12.pdf) | [Part 1]()   |   [Part 2]() | Direct method: example. General existence theorem | +| 9 June | [Lesson 13](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_13.pdf) | [Part 1]()   |   [Part 2]() | LSC Envelope. Relaxation and its computation | +| 16 June | [Lesson 14](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_14.pdf) | [Part 1]()   |   [Part 2]() | Relaxation of integral functionals. $$\Gamma$$-convergence | +| 23 June | [Lesson 15](/assets/pdf/teaching/2021-Calculus-of-Variations/lecture_notes/lesson_15.pdf) | [Part 1]()   |   [Part 2]() | Examples of $$\Gamma$$-convergence. Homogenization problems | Calculus of Variations 2020/21 | Lesson 1 | Part 1