Functional Analysis and Applications ::.
The general aim of the group is to perform research in the fields of boundary value problems, differential equations and inclusions, function spaces, integral transforms and equations, operator theory, and variational problems, as well as their applications

In a more detailed way, the group performs research in:

BOUNDARY VALUE PROBLEMS (BVPs): Existence and multiplicity of solutions to BVPs; BVPs for elliptic systems of differential equations (including those for linearized elasticity, for the Stokes system, and on the Heisenberg group); BVPs for the Helmholtz equation and p-Laplacian; Potential theory techniques in BVPs; Schrödinger-Poisson systems, and systems with Radon measure

DIFFERENTIAL INCLUSIONS: Extremal solutions to nonconvex differential inclusions by probabilistic methods; solutions to nonconvex differential inclusions with the p-Laplacian

FUNCTION SPACES (FS): FS of generalized and variable smoothness; FS of variable integrability; FS over fractals and quasi-metric spaces; box and Hausdorff dimensions of graphs of functions in FS; selected operators on irregular/fractal domains and their spectra; approximation theory

INTEGRAL TRANSFORMS AND EQUATIONS: Integral equations of several different kinds (with oscillatory kernels, special functions, etc.), new integral transforms, uncertainty principles, new convolutions and norm inequalities

OPERATOR THEORY: Singular integral operators with shift, Wiener-Hopf plus/minus Hankel operators (also on spaces of variable integrability); pseudo-differential operators; operator relations; wave diffraction problems from an operator theory viewpoint; Fredholm property characterization of classes of operators

VARIATIONAL PROBLEMS: Existence and regularity of solutions to minimum problems for integral functionals depending on the gradient with slow growth; minimization of functionals constrained by non-convex differential inclusions

CONCRETE APPLICATIONS (examples which are going on): Measurement of efficiency of public Hospitals and energy (e.g. in European countries), new SIR-type models for governance, and modelling the size and shapes of animals (with a set of laws allowing algebraisation)



The group runs a biweekly seminar during lecture time, with the concern that the majority of speakers come from outside the R&D Unit and a not negligible percentage of these do their research activities outside the country.

There is also an Annual workshop of the Group

The 2017 workshop will be on April 10.

Contacts:
Prof. Doutor Luís Filipe Pinheiro de Castro
phone: (+351) 234370683
Fax: (+351) 234382014
e-mail: castro@ua.pt

Conference IDOTA2011: Integral and Differential Operators and Their Applications
- An International Conference in Honour of Professor Stefan Samko on the occasion of his 70th birthday (100 participants and 70 talks), University of Aveiro, Portugal, 30 June - 2 July, 2011. http://idota2011.glocos.org/
2011-06-30
FIRST ANNUAL WORKSHOP of Functional Analysis and Applications Group
This is the annual workshop of the Functional Analysis and Applications group where it is desirable that all the PhD members of the group and their PhDs students present a short talk (which may include open problems) - followed by discussion - in view of exchanging ideas and fomenting further research plans. The speakers of this first edition were Luís Castro, Anabela Silva, Alberto Simões, Ana Paula Nolasco, Saburou Saitoh, Anabela Ramos, António Caetano, Alexandre Almeida, Sofia Lopes, Vítor Neves, Vasile Staicu, Manuela Rodrigues, Jianqing Chen, Kelly Murillo, and Eugénio Rocha
2010-05-15
SECOND ANNUAL WORKSHOP of Functional Analysis and Applications Group
This is the annual workshop of the Functional Analysis and Applications group where it is desirable that all the PhD members of the group and their PhDs students present a short talk (which may include open problems) - followed by discussion - in view of exchanging ideas and fomenting further research plans. Poster of the Workshop. Date: October 29, 2011
2011-10-29
THIRD ANNUAL WORKSHOP of Functional Analysis and Applications Group
This is the annual workshop of the Functional Analysis and Applications group where it is desirable that all the PhD members of the group and their PhDs students present a short talk (which may include open problems) - followed by discussion - in view of exchanging ideas and fomenting further research plans. Date: October 27, 2012. Programme of the Workshop
2012-10-27
 
 
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