Fabio Silva Botelho,
PhD
Professor Adjunto,
Departamento de Matemática
Universidade Federal
de Santa Catarina  UFSC
Cálculo
Variacional
Horário
2019/1  Tópicos em Cálculo Variacional e Otimização
em Espaços de Banach
Terças 18 h –
20 h 30 min
e Quintas 16 h –
18 h 30 min
Sala CFM A 11 –
Ambos os dias
Análise
Funcional – Curso de Verão – 2019 – Notas de
Aula, Listas de Exercícios e resultados da segunda avaliação
de 1/3/2019
Análise
Funcional Aplicada
Cálculo
1 – notas de aula
Cálculo
1 – 20182  Listas de exercícios Resultados  REC
Cálculo
2 – 20182 Listas de exercícios Resultados da P3
PAM
– Listas de exercícios
Livros:
Functional
Analysis and Applied Optimization in Banach Spaces, Springer 2014.
Book
review
Real
Analysis and Applications, Springer 2018.
A
Classical Description of Variational Quantum Mechanics and Related
Models, Nova Science Publishing, 2017.
This work is
dedicated in memoriam to David Bohm and Jiddu Krishnamurti
Preprints –
Physics
 1. arXiv:1812.04097
[pdf, ps,
other]

A variational formulation for relativistic mechanics based on
Riemannian geometry and its application to the quantum mechanics
context

Fabio
Botelho

Comments: 15 pages, new results based on the Weinberg approach for
relativistic mechanics

Subjects: Analysis of PDEs (math.AP)
2. A
Variational Formulation for the Relativistic KleinGordon Equation
This is the correct
, revised (submitted) version.
For some reason the
Journal Ciência e Natura published a previous not revised
version.
Also, for this
article, the journal has indicated in its webpage:
Article received
04/12/2017 (day,month,year)
Article Accepted:
05/06/2018
For the other
article published, they have indicated:
Article received:
04/08/2017
Article Accepted:
04/09/2018
Indeed these dates
are not correct. The two articles I have published in this journal
were both submitted about April/May 2018 and accepted
about 45 days after
submission with a GAP of about 30 days between the acceptances.
Also, the journal
did not present the proofs of both articles to the author for
verification and final agreement.
PreprintsApplied
Mathematics
1. arXiv:1904.02286
[pdf, ps,
other]
math.OC
A primal dual variational formulation and a multiduality
principle for a nonlinear model of plates
Authors: Fabio
Botelho
Submitted 18 April, 2019; v1 submitted 3 April, 2019; originally
announced April 2019.
Comments: 20 pages, some typos corrected, a new result added
MSC Class: 49N15; 74P99
 2. arXiv:1903.06014
[pdf, ps,
other]

A duality principle for nonconvex optimization in Rn

Fabio
Botelho

Comments: 13 pages, some typos and errors corrected, in this version
all proof details have been provided

Subjects: Optimization and Control (math.OC)

3. arXiv:1902.08811
[pdf, ps,
other]

A note on optimization in Rn

Fabio
Botelho

Comments: 10 pages

Subjects: Optimization and Control (math.OC)

4. arXiv:1902.04448
[pdf, ps,
other]

Existence of solution for an optimal control problem associated to
the GinzburgLandau system in superconductivity

Fabio
Botelho, Eduardo
Pandini Barros

Comments: 8 pages

Subjects: Optimization and Control (math.OC)

5. arXiv:1812.04097
[pdf, ps,
other]

A variational formulation for relativistic mechanics based on
Riemannian geometry and its application to the quantum mechanics
context

Fabio
Botelho

Comments: 15 pages, new results based on the Weinberg approach for
relativistic mechanics

Subjects: Analysis of PDEs (math.AP)

6. arXiv:1809.09575
[pdf, ps,
other]

On central fields in the calculus of variations

Fabio
Botelho

Comments: 12 pages, typos corrected

Subjects: Optimization and Control (math.OC)

7. arXiv:1804.06283
[pdf, ps,
other]

On General Duality Principles for NonConvex Variational
Optimization with Applications to the GinzburgLandau System in
Superconductivity

Fabio
Botelho

Comments: 32 pages, typos corrected, other results added

Subjects: Optimization and Control (math.OC)

8. arXiv:1712.04809
[pdf, ps,
other]

A duality principle for a semilinear model in micromagnetism

Fabio
Botelho

Comments: 7 pages

Subjects: Optimization and Control (math.OC)

9. arXiv:1712.03552
[pdf, ps,
other]

On the numerical solution of nonlinear first order ordinary
differential equation systems

Fabio
Botelho

Comments: 9 pages

Subjects: Numerical Analysis (math.NA)

10. arXiv:1712.02701
[pdf, ps,
other]

A duality principle for nonlinear elasticity

Fabio
Botelho

Comments: 10 pages, more typos and errors corrected, some parts of
the text have been rewritten

Subjects: Optimization and Control (math.OC)

11. arXiv:1712.01595
[pdf, ps,
other]

Global existence results and duality for nonlinear models of plates
and shells

Fabio
Botelho

Comments: 28 pages, some parts of the text have been rewritten,
variational nature of the dual formulations retaken

Subjects: Analysis of PDEs (math.AP); Optimization and Control
(math.OC)


This
work is dedicated in memoriam to Professor J.J. Telega


12. arXiv:1712.01031
[pdf, ps,
other]

On duality principles for nonconvex variational models applied to a
GinzburgLandau type equation

Fabio
Botelho

Comments: 14 pages, more typos corrected

Subjects: Optimization and Control (math.OC)
Artigos completos publicados em periódicos
1. Fabio Botelho,
A
note on Riemannian geometry and the relativistic quantum mechanics
context. CIÊNCIA E NATURA, v. 40, p. 58, 2018.
2. Fabio
Botelho.,A
Variational Formulation for the Relativistic KleinGordon Equation.
CIÊNCIA E NATURA, v. 40, p. 57, 2018.
3. Fabio Botelho,
On
the Generalized Method of Lines Applied to GinzburgLandau Type
Equations. International Journal of Applied and Computational
Mathematics, v. 1, p. pp 115, 2016.
4. Lucas dos
Santos Fernandez, Alexandre Molter, Fabio Silva Botelho,
Simultaneous
topology optimization and proportional actuators localization. SeMA
Journal, v. 23, p. , 2016.
5. Fabio Botelho,
On
the Lagrange multiplier theorem in Banach spaces. Matemática
Aplicada e Computacional (Cessou em 1997. Cont. ISSN 18070302
Computational & Applied Mathematics)^{
},
v. 32, p. 135144, 2013.
6. Fabio Botelho.
Existence
of solution for the Ginzburg Landau system, a related optimal control
problem and its computation by the generalized method of lines.
Applied Mathematics and Computation^{
},
v. 218, p. 1197611989, 2012.
7. Fabio Botelho,
On
duality principles for scalar and vectorial multiwell variational
problems. Nonlinear Analysis^{
},
v. 75, p. 19041918, 2012.
8. Fabio Botelho, Dual
Variational Formulations for a Nonlinear Model of Plates. JOURNAL OF
CONVEX ANALYSIS^{
},
v. 17, p. 131158, 2010.