Well-posedness theory for the weakly harmonic maps problem subject to irregular data

Abstract: We study the existence, uniqueness and regularity of weakly harmonic maps into a closed Riemannian manifold. In this talk, I will emphasize on the novel ideas, based on intrinsic features of the problem and modern harmonic analysis tools which allow us to prescribe Dirichlet data with infinite energy. More precisely, we prove that under a mere smallness hypothesis on the boundary data measured in the $L^{\infty}$ or $BMO$ norm, there exists a unique solution which is locally infinitely smooth. While this regularity feature fails in absence of the smallness assumption, existence still persists for large data provided the domain is bounded and there exist smooth stable weakly harmonic maps. This is a joint work with Herbert Koch.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php