Andreas Rosén
My research mostly concerns Partial Differential Equations, and uses techniques from harmonic analysis and operator theory. A central problem is the well posedness of boundary value problems for PDEs with non-smooth coefficients or domains. With functional calculus and harmonic analysis we construct new operators beyond singular integrals, with which non-smooth PDEs can be solved constructively.
My focus is on systems of first order PDEs, motivated by Dirac operators from mathematical physics. In algebra and geometry I work much with differential forms, exterior algebra, Clifford algebra and spinors.
Showing 19 publications
Causal sparse domination of Beurling maximal regularity operators
An efficient full-wave solver for eddy currents
Comparison of integral equations for the Maxwell transmission problem with general permittivities
Dirac Integral Equations for Dielectric and Plasmonic Scattering
Boosting the Maxwell double layer potential using a right spin factor
Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric
Bounded variation approximation of Lp Dyadic martingales and solutions to elliptic equations
Evolution of Time-Harmonic Electromagnetic and Acoustic Waves Along Waveguides
A spin integral equation for electromagnetic and acoustic scattering
A local Tb theorem for matrix weighted paraproducts
Teaching and Learning Electromagnetics: An Analytical Problem-Solving Approach
BOUNDARY VALUE PROBLEMS FOR DEGENERATE ELLIPTIC EQUATIONS AND SYSTEMS
Cauchy integrals for the p-Laplace equation in planar Lipschitz domains
Layer potentials beyond singular integral operators
Square function and maximal function estimates for operators beyond divergence form equations
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