Pointwise convergence of solutions to the nonelliptic Schrodinger equation Keith RogersAna VargasLuis Vega 35Q5542B25Schr\"odinger equationpointwise convergence It is conjectured that the solution to the Schr\"odinger equation in $\mathbb{R}^{n+1}$ converges almost everywhere to its initial datum $f$, for all $f \in H^{s}(\mathbb{R}^n)$, if and only if $s \ge \frac{1}{4}$. It is known that there is an $s < \frac{1}{2}$ for which the solution converges for all $f \in H^{s}(\mathbb{R}^{2})$. We show that the solution to the nonelliptic Schr\"odinger equation, $i\partial_{t}u + (\partial^{2}_{x} - \partial^{2}_{y})u = 0$, converges to its initial datum $f$, for all $f \in H^{s}(\mathbb{R}^{2})$, if and only if $s \ge \frac{1}{2}$. Thus the pointwise behaviour is worse than that of the standard Schr\"odinger equation. In higher dimensions, we have similar results with the loss of the endpoint. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2827 10.1512/iumj.2006.55.2827 en Indiana Univ. Math. J. 55 (2006) 1893 - 1906 state-of-the-art mathematics http://iumj.org/access/