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)