Abstract We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.

中文翻译：

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时域上波动方程的最小化方法

摘要 我们证明了在一类合适的瞬态域上齐次波动方程的弱解的存在。使用 De Giorgi 建议并由 Serra 和 Tilli 开发的方法，此类解决方案由时空中合适泛函的最小化器逼近。