Sumários

No lecture scheduled

3 Abril 2019, 15:30 • José Francisco da Silva Costa Rodrigues

No lecture scheduled

No lecture scheduled

28 Março 2019, 14:30 • José Francisco da Silva Costa Rodrigues

No lecture scheduled

A desigualdade isoperimétrica

27 Março 2019, 17:00 • José Francisco da Silva Costa Rodrigues

Isoperimetric inequality
The Wringer inequality in one dimension and the planar isoperimetric inequality; the isoperimetric inequality in higher dimensions based on the Brunn-Minkoswski theorem.
Proposed exercises: 6.2.2 and 6.2.3 (p.160) and 6.3.2 (p.168) of Chap. 6 of the Dacorogna's 2004 ICP book.
Discussions on exercises of previous lectures.

A desigualdade isoperimétrica

27 Março 2019, 15:30 • José Francisco da Silva Costa Rodrigues

Isoperimetric inequality
The Wringer inequality in one dimension and the planar isoperimetric inequality; the isoperimetric inequality in higher dimensions based on the Brunn-Minkoswski theorem.
Proposed exercises: 6.2.2 and 6.2.3 (p.160) and 6.3.2 (p.168) of Chap. 6 of the Dacorogna's 2004 ICP book.
Discussions on exercises of previous lectures.

Questões de regularidade e de superfícies mínimas no Cálculo da Variações

21 Março 2019, 14:30 • José Francisco da Silva Costa Rodrigues

Questions of  regularity and minimal sufaces mínimas no Cálculo da Variações


Part 1: Regularity issues arising from the direct method in the Calculus of Variations: the one dimensional case, from the quadratic case with a semi-linear variational term to a general convex case; the Dirichlet integral in n-dimensions and the relations with the elliptic theory of PDEs.
Proposed exercises: 4.2.1 (p.117) and 4.3.2 and 4.3.3 (p.123).
Suggested reading: G. Stampacchia, Hilbert twenty-third problem extensions of the Calculus of Variations, Proceeding of Symposia in Pure Mathematics, vol 28 Part 2 (1976), American Mathematical Society. (see the PDF in Fenix)

Part 2: Classical applications in Geometry: introduction to minimal surfaces in the parametric and nonparametric form; classical solutions and variational formulations; main ideas of the Douglas-Courant-Tonelli method—this was part of a seminar presentation of Luis Sampaio.
Proposed exercises 5.2.4 (p. 139).

Note. This lecture took place the 22nd March 2019, 14:00—17:00, room 6.2.33 and was based on reading Chapters 4 and 5 of Dacorogna's 2004 ICP book.