CORDIS provides links to public deliverables and publications of HORIZON projects.
Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .
Exploitable results
Boundary value problems for partial differential equations in several complex variables are for the first time explicitly solved. For overdetermined systems necessary and sufficient conditions on the nonhomogeneities as well of the system as of the boundary condition are given so that the problems are solvable. Explicit solutions are given for the cases of the ball and the polydisc. Among these problems are the Schwarz, the Riemann-Hilbert, the Dirichlet and the Neumann problem. Also new boundary value problems are solved. Among the systems treated are mainly first and second order, complete and uncompleted overdetermined elliptic, but also nonelliptic systems. Higher order Cauchy Pompeiu representations well known for one complex variable are given as well for several complex variables in the case of polydomains, for Douglis-algebra valued and for Clifford-algebra valued, functions by defining proper Newton-type potentials.
A reproducing kernel is given for the monogenic counterpart of the Segal-Bargman pace and the isometry operator with the classical Segal-Bargman space investigated. Clifford analysis is extended to the indefinite space Rpq and the uniqueness property of the Cauchy kernel in quaternionic, in Clifford analysis, and in several complex variables explained. Models of linear dynamical systems with multidimensional discrete time based on an appropriate function theory is constructed.
Hypercomplex differentiability is extended to treat systems of partial differential equations from mathematical physics. Integral representations for solutions to the Dirichlet problem for biquaternionic hypercomplex differentiable functions are given. Boundary properties of integral operators characterizing the Dirac spinor fields are derived and the results applied to models of quartz confinement as e.g. the MIT bag model.
Dubinskij's results on Leray-Volevich conditions for systems of pseudodifferential equations are generalized to systems of evolution equations with generalized derivatives in the sense of Gelfond-Leontjev. By complex analytic methods (Riemann-Hilbert-Poincaré boundary value problems) and Banach scale techniques the existence of local solutions in time to the Hele Shaw problem is shown. Solutions of the regularized and the unregilarised models are compared to determine critical times and succing rates.
Boundary value problems for the Moisil-Theodorescu and the Solomjak system are treated. Fredholm and quasi-Fredholm property respectively could be proved. Boundary value problems for singular Vekua-type equations were studied by model equations without any smallness conditions and without glueing procedure.
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