We present a new approach for boundary integral equations for the wave equation with zero initial conditions. Unlike previous attempts, our mathematical formulation allows us to prove that the associated boundary integral operators are continuous and satisfy inf-sup conditions in trace spaces of the same regularity, which are closely related to standard energy spaces with the expected regularity in space and time. This feature is crucial from a numerical perspective, as it provides the foundations to derive sharper error estimates and paves the way to devise efficient adaptive space-time boundary element methods, which will be tackled in future work. On the other hand, the proposed approach is compatible with current time dependent boundary element method's implementations and we predict that it explains many of the behaviours observed in practice but that were not understood with the existing theory.

翻译：与先前的尝试不同,我们的数学公式让我们能够证明相关的边界整体操作员是连续不断的,并且符合同一规律性微小空间的内溢条件,这些空间与标准能源空间密切相关,而且预计时空的规律性。 从数字角度看,这一特征至关重要,因为它为得出更清晰的误差估计提供了基础,并为设计高效的适应性空间-时间边界要素方法铺平了道路,这些方法将在今后的工作中处理。另一方面,拟议方法与当前取决于时间的边界要素方法的实施相兼容,我们预测它解释了实践中观察到的许多行为,但与现有理论不理解。