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 2022 workshop occurred on September 28, 2022.

Scientific Group Leader:

Luís Filipe Pinheiro de Castro
e-mail: castro@ua.pt




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