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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
79/2014

Estimates for solutions of Dirac equations and an application to a geometric elliptic-parabolic problem

Qun Chen, Jürgen Jost, Linlin Sun and Miaomiao Zhu

Abstract

We develop estimates for the solutions and derive existence and uniqueness results of various local boundary value problems for Dirac equations that improve all relevant results known in the literature. With these estimates at hand, we derive a general existence, uniqueness and regularity theorem for solutions of Dirac equations with such boundary conditions. We also apply these estimates to a new nonlinear elliptic-parabolic problem, the Dirac-harmonic heat flow on Riemannian spin manifolds. This problem is motivated by the supersymmetric nonlinear $\sigma$-model and combines a harmonic heat flow type equation with a Dirac equation that depends nonlinearly on the flow.

Received:
Aug 18, 2014
Published:
Aug 18, 2014
MSC Codes:
58E20, 35J56, 35J57, 53C27
Keywords:
Dirac equation, existence, uniqueness, chiral boundary condition, Dirac-harmonic map flow

Related publications

inJournal
2019 Repository Open Access
Qun Chen, Jürgen Jost, Linlin Sun and Miaomiao Zhu

Estimates for solutions of Dirac equations and an application to a geometric elliptic-parabolic problem

In: Journal of the European Mathematical Society, 21 (2019) 3, pp. 665-707