Skip to main content
If you continue browsing this website, you agree to our policies:
Condizioni di utilizzo e trattamento dei dati
Continue
x
English (en)
English (en)
Français (fr)
Italiano (it)
You are currently using guest access
Log in
Macroarea STEM
Home
Calendar
Unipd
Educational Offer
Timetables
Uniweb
Webmail
My Media
Home
Calendar
Unipd
Educational Offer
Timetables
Uniweb
Webmail
My Media
More
Expand all
Collapse all
Open course index
FUNCTIONS THEORY
Course record
Course record
Section outline
Select activity 29/09: Space of continuous functions, and sup norm. Ascoli Arzela' compactness theorem. The space of test functions
29/09: Space of continuous functions, and sup norm. Ascoli Arzela' compactness theorem. The space of test functions
File
Select activity 6/10: test functions are dense in L^p. DuBois Reymond lemma (added a page)
6/10: test functions are dense in L^p. DuBois Reymond lemma (added a page)
File
Select activity 7/10: partitions of unity. Open sets of class C^k, signed distance, exterior and interior sphere condition
7/10: partitions of unity. Open sets of class C^k, signed distance, exterior and interior sphere condition
File
Select activity 8/10: integration on sphere formula. Borel measures and Radon measures.
8/10: integration on sphere formula. Borel measures and Radon measures.
File
Select activity 13/10: Positive linear functionals on C_c(U). Riesz theorem on Radon measure. Weak compactness in the space of Radon measure. Recall of L^p weak, weak^* compactness theorems.
13/10: Positive linear functionals on C_c(U). Riesz theorem on Radon measure. Weak compactness in the space of Radon measure. Recall of L^p weak, weak^* compactness theorems.
File
Select activity 14/10: embedding of L^1 in the space of signed Radon measures and weak compactness thm; Lebesgue theorem, Meaure theoretic boundary and topological boundary.
14/10: embedding of L^1 in the space of signed Radon measures and weak compactness thm; Lebesgue theorem, Meaure theoretic boundary and topological boundary.
File
Select activity 15/10: absolutely continuous measures and singular measures, density of an a.c. measuure, Lebesgue-Radon-Nikodym decomposition. Hausdorff measures.
15/10: absolutely continuous measures and singular measures, density of an a.c. measuure, Lebesgue-Radon-Nikodym decomposition. Hausdorff measures.
File
Select activity 20/10:Hausdorff dimension of a set. Example of the Cantor set and devil's staircase (without proof of the Hausdorff dimension)
20/10:Hausdorff dimension of a set. Example of the Cantor set and devil's staircase (without proof of the Hausdorff dimension)
File
Select activity 21/10: Isodiametric inequality in R^n by Steiner symmetrization. Proof that H^n is Lebesgue on R^n
21/10: Isodiametric inequality in R^n by Steiner symmetrization. Proof that H^n is Lebesgue on R^n
File
Select activity 22/10: H^k rectifiable sets.Definition of distribution. Order of a distribution.
22/10: H^k rectifiable sets.Definition of distribution. Order of a distribution.
File
Select activity 27/10: order of a distribution, example of distributions, principal value. Derivative of a distribution
27/10: order of a distribution, example of distributions, principal value. Derivative of a distribution
File
Select activity 28/10: weak derivatives and derivatives in the sense of distributions.
28/10: weak derivatives and derivatives in the sense of distributions.
File
Select activity 29/10: Cantorian measures. Convolution of a distribution and a test function
29/10: Cantorian measures. Convolution of a distribution and a test function
File
Select activity Cantor function (Ambrosio, Fusco, Pallara book)
Cantor function (Ambrosio, Fusco, Pallara book)
File
Select activity 3/11: density of test functions in the space of distributions. Fundamental solution of a differential operator.
3/11: density of test functions in the space of distributions. Fundamental solution of a differential operator.
File
Select activity 4/11: Fundamental solution of the laplacian. Introduction to Sobolev spaces.
4/11: Fundamental solution of the laplacian. Introduction to Sobolev spaces.
File
Select activity 4/11 problem session
4/11 problem session
File
Select activity 5/11: Sobolev spaces in dimension 1.
5/11: Sobolev spaces in dimension 1.
File
Select activity 17/11: density of smooth functions. Gagliardo, Nirenberg, Sobolev inequality.
17/11: density of smooth functions. Gagliardo, Nirenberg, Sobolev inequality.
File
Select activity 18 and 19 november: GNS inequality and Poincare' inequality. First eigenvalue of the laplacian with Dirichlet bdry conditions (Ref. Evans PDE ch, 6, thm 2)
18 and 19 november: GNS inequality and Poincare' inequality. First eigenvalue of the laplacian with Dirichlet bdry conditions (Ref. Evans PDE ch, 6, thm 2)
File
Select activity 24/11: Morrey inequality and consequences
24/11: Morrey inequality and consequences
File
Select activity 25/11: Lipschitz continuous functions and W^{1, infty}, Rademacher theorem
25/11: Lipschitz continuous functions and W^{1, infty}, Rademacher theorem
File
Select activity 26/11: extension and traces for Sobolev functions
26/11: extension and traces for Sobolev functions
File
Select activity 1/12: Continuous embeddings for W^{1,p}(U), U bdd of class C^1. Compact embeddings.
1/12: Continuous embeddings for W^{1,p}(U), U bdd of class C^1. Compact embeddings.
File
Select activity 2/12: proof of Rellich-Kondrachov theorem. Corollary (W^{1,p} is compactly embedded in L^p)).
2/12: proof of Rellich-Kondrachov theorem. Corollary (W^{1,p} is compactly embedded in L^p)).
File
Select activity 3/12: a classical example from Calculus of Variations. Poincare' inequality
3/12: a classical example from Calculus of Variations. Poincare' inequality
File
Select activity 9/12: W^1,n is continuously embedded in BMO. The harmonic extension of a W^1,2 function.
9/12: W^1,n is continuously embedded in BMO. The harmonic extension of a W^1,2 function.
File
Select activity 10/12: the space of BV functions
10/12: the space of BV functions
File
Select activity 15/12:strong convergence, strict convergence and weak star convergence in BV. BV functions in dimension 1.
15/12:strong convergence, strict convergence and weak star convergence in BV. BV functions in dimension 1.
File
Select activity 16/12: BV functions in dim>1: density in strict sense of W^{1,1}, GNS inequality, compactness theorem
16/12: BV functions in dim>1: density in strict sense of W^{1,1}, GNS inequality, compactness theorem
File
Select activity 16/12: problem session
16/12: problem session
File
Select activity 17/12: Sets of finite perimeter. Main properties.
17/12: Sets of finite perimeter. Main properties.
File