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 2018 workshop occurred on October 24, 2018.
Contacts:
Prof. Doutor António Manuel Rosa Pereira Caetano
e-mail: acaetano@ua.pt