On the Cauchy problem for the heat equation on Riemannian manifolds with conical singularities
On the Cauchy problem for the heat equation on Riemannian manifolds with conical singularities
复制标题
具有圆锥奇点的黎曼流形热方程的柯西问题
DOI：
10.1093/qmath/has016
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Tapio Behrndt
中科院分区：
文献类型：
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作者：
Tapio Behrndt
研究了紧致黎曼流形上具有锥奇点的非齐次热方程Cauchy问题解的存在性和正则性。引入了具有离散渐近性的加权H“older空间和Sobolev空间，证明了当自由项位于具有离散渐近性的加权抛物H“older空间或Sobolev空间中时，非齐次热方程Cauchy问题解的存在性和极大正则性.这推广了Coriasco，Schrohe和Seiler（Thm. 7.2在数学Z. 244（2003），235- 269）。
We study the existence and regularity of solutions to the Cauchy problem for the inhomogeneous heat equation on compact Riemannian manifolds with conical singularities. We introduce weighted H\"older and Sobolev spaces with discrete asymptotics and we prove existence and maximal regularity of solutions to the Cauchy problem for the inhomogeneous heat equation, when the free term lies in a weighted parabolic H\"older or Sobolev space with discrete asymptotics. This generalizes a result previously obtained by Coriasco, Schrohe, and Seiler (Thm. 7.2 in Math. Z. 244 (2003), 235--269) by different means.