Invariance of closed convex sets and domination criteria for semigroups
Invariance of closed convex sets and domination criteria for semigroups
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闭凸集的不变性和半群的支配准则
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发表时间：
1996
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通讯作者：
E. Ouhabaz
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作者：
E. Ouhabaz
设a和b是希尔伯特空间H=L2(Ω, μ)上的两个正连续且封闭的倍半线性形式。用 T=T(t)t≥0 和 S=S(t)t≥0 表示由 a 和 b 在 H 上生成的半群。我们根据 a 和 b 给出准则，保证半群 T 由 S 支配，即 |T(t)f|≤S(t)|f|对于所有 t≧0 且 f∈H。所提出的方法利用了半群下 H 的闭凸集不变性的思想。给出了椭圆算子的应用和具体例子。
Let a and b be two positive continuous and closed sesquilinear forms on the Hilbert space H=L2(Ω, μ). Denote by T=T(t)t≧0and S=S(t)t≧0the semigroups generated by a and b on H. We give criteria in terms of a and b guaranteeing that the semigroup T is dominated by S, i.e. |T(t)f|≦S(t)|f| for all t≧0 and f∈H. The method proposed uses ideas on invariance of closed convex sets of H under semigroups. Applications to elliptic operators and concrete examples are given.