Free boundary regularity below the continuous threshold: 2-phase problems
Free boundary regularity below the continuous threshold: 2-phase problems
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低于连续阈值的自由边界正则性：两相问题
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
T. Toro
中科院分区：
文献类型：
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作者：
C. Kenig;T. Toro
本文继续研究调和测度和Poisson核在连续阈值以下的自由边界正则性问题。我们将注意力集中在两阶段问题上。我们证明了在自由边界数据的适当假设下，如果每一相是几何非简并的，则自由边界是规则的。这项工作的主要新观点是，自由边界上的平坦性条件不是先验假设的。
Abstract In the present paper we continue our study of free boundary regularity problems for harmonic measure and Poisson kernels, below the continuous threshold. We focus our attention on 2-phase problems. We show that under the appropriate hypothesis for the free boundary data, if each phase is geometrically non-degenerate then the free boundary is regular. The main new point of this work is that no flatness condition on the free boundary is assumed a priori.