Modulus of continuity of the Dirichlet solutions
Modulus of continuity of the Dirichlet solutions
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DOI：
10.1112/blms/bdq040
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发表时间：
2009-09
影响因子：
0.9
通讯作者：
Hiroaki Aikawa
中科院分区：
文献类型：
--
作者：
Hiroaki Aikawa
设D是n ∈ N中的有界区域，n ∈ N ≥ 2.对于f在D上的函数f，我们用f表示D上f的狄利克雷解。经典的是，如果D是正则的，则将连续边界函数族映射到D中连续到边界的调和函数族。我们表明，改进的边界函数f的连续性，确保改进的连续性，在一般模的连续性的背景下，f的连续性。
Let D be a bounded domain in ℝn with n ⩾ 2. For a function f on ∂D we denote by ℋD f the Dirichlet solution, for the Laplacian, of f over D. It is classical that if D is regular, then ℋD maps the family of continuous boundary functions to the family of harmonic functions in D continuous up to the boundary ∂D. We show that improved continuity of a boundary function f ensures improved continuity of ℋD f in the context of general modulus of continuity.