A Remark on Nonlinear Dirac Equations

Details A Remark on Nonlinear Dirac Equations A Remark on Nonlinear Dirac Equations

2008-10-11

arxiv.org/abs/0810.2051v1

Mathematics

Analysis of PDEs

6pages

Scientific paper

For a $n$-dimensional spin manifold $M$ with a fixed spin structure and a
spinor bundle $\Sigma M$, we prove an $\epsilon$-regularity theorem for weak
solutions to the nonlinear Dirac equation of cubic nonlinearity. This, in
particular, answers a regularity question raised by Chen-Jost-Wang when $n=2$.

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