A priori $L^p$ estimates for solutions of Riemann-Hilbert Problems

Mathematics – Classical Analysis and ODEs

Scientific paper

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Scientific paper

The authors use steepest descent ideas to obtain a priori $L^p$ estimates for
solutions of Riemann-Hilbert Problems. Such estimates play a crucial role, in
particular, in analyzing the long-time behavior of solutions of the perturbed
nonlinear Schr\"odinger equation on the line.

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