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

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

  • BOUNDARY VALUE PROBLEMS (BVPs): Existence and multiplicity of solutions; systems of elliptic equations; Helmholtz equation; problems with the (fractional) p-Laplacian.
  • DIFFERENTIAL INCLUSIONS: Gradient inclusions; periodic solutions for differential inclusions with the p-Laplacian.
  • FUNCTION SPACES (FS): of generalized or variable smoothness; of variable integrability; FS over fractals or quasi-metric spaces; operators on irregular/fractal domains and their spectra.
  • OPERATOR THEORY: Singular integral operators with shift, Wiener-Hopf plus/minus Hankel operators; pseudo-differential operators; operator relations; wave diffraction problems from an operator theory viewpoint; Fredholm property characterization of classes of operators.
  • REPRODUCING KERNEL HILBERT SPACES THEORY (RKHST): Application of RKHST techniques to integral equations of several different kinds, integral transforms and differential equations; fractional functions representations by means of RKHST; new convolutions and norm inequalities by using RKHST.

Applications outside mathematics have also been made, e.g. to Chemistry, Civil Engineering and Econometrics.

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 2018 workshop occurred on October 24, 2018.

Scientific Group Leader:

António Manuel Rosa Pereira Caetano
e-mail: acaetano@ua.pt



Previous Seminars
14 Jun 2019
Roland Duduchava - The University of Georgia & A. Razmadze Mathematical Institute,Tbilisi, Georgia

07 Jun 2019
Teresa Faria - Departamento de Matemática & CMAF-CIO, Faculdade de Ciências, Universidade de Lisboa

10 May 2019
Cláudio Fernandes, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa

26 Apr 2019
José J. Oliveira


© 2019 CIDMA, all rights reserved