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首页> 外文期刊>Philosophical transactions of the Royal Society. Mathematical, physical, and engineering sciences >Regularity of free boundaries a heuristic retro
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Regularity of free boundaries a heuristic retro

机译：自由边界的规律性启发式复古

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摘要

This survey concerns regularity theory of a few free boundary problems that have been developed in the past half a century. Our intention is to bring up different ideas and techniques that constitute the fundamentals of the theory. We shall discuss four different problems, where approaches are somewhat different in each case. Nevertheless, these problems can be divided into two groups: (i) obstacle and thin obstacle problem; (ii) minimal surfaces, and cavitation flow of a perfect fluid. In each case, we shall only discuss the methodology and approaches, giving basic ideas and tools that have been specifically designed and tailored for that particular problem. The survey is kept at a heuristic level with mainly geometric interpretation of the techniques and situations in hand.
机译：这项调查涉及过去半个世纪中发展出来的一些自由边界问题的规律性理论。我们的目的是提出构成理论基础的不同思想和技术。我们将讨论四个不同的问题，每种情况下的方法有所不同。然而，这些问题可以分为两类：（i）障碍和薄障碍问题; （ii）最小的表面和完美流体的空化流。在每种情况下，我们将仅讨论方法论和方法，给出针对特定问题专门设计和定制的基本思想和工具。该调查处于启发式级别，主要对手头的技术和情况进行几何解释。

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