ON THE SINE-GORDON — THIRRING EQUIVALENCE IN THE PRESENCE OF A BOUNDARY

In this paper, the relationship between the sine-Gordon model with an integrable boundary condition and the Thirring model with boundary is discussed and the reflection R matrix for the massive Thirring model, which is related to the physical boundary parameters of the sine—Gordon model, is given. The relationship between the boundary parameters and the two formal parameters appearing in the work of Ghoshal and Zamolodchikov is also discussed.

The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition

The Poisson integral of a Denjoy-Perron integrable function defined on the boundary of an open disc is harmonic in this disc. Moreover, almost everywhere on the boundary, the nontangential limits of the integral coincide with the boundary condition. This extends the classical result for Lebesgue integrable boundary conditions. By means of conformai maps, a generalization to domains bounded by a sufficiently smooth Jordan curve is also obtained.