Functional Analysis and Applications ::.
Year: 2017
2020   2019   2018   2017 

RESEARCH: Research Topics and Projects

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)

Research Topics and Projects
desenvolvido por: Mentes Virtuais