An asymptotic mean value characterization for p-harmonic functions
An asymptotic mean value characterization for p-harmonic functions
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DOI：
10.1090/s0002-9939-09-10183-1
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发表时间：
2010-03
期刊：
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通讯作者：
J. Manfredi;M. Parviainen;J. Rossi
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文献类型：
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作者：
J. Manfredi;M. Parviainen;J. Rossi
我们用一个渐近均值性质来刻画p-调和函数。P-调和函数u是Δp u=∇(|∇u|p-2≤∞u)=0的粘性解，其中1<；pΩ在区域α中当且仅当展开u(X)=β/2{max/Be(X)u+∫/Be(X)u}+→/|Be(X)|αBe(X)udy+o(E2)在弱意义下对xβ成立e∫0，我们称之为粘性意义。这里，系数α，β由α+β=1和α/β=(p-2)/(N+2)确定。
We characterize p-harmonic functions in terms of an asymptotic mean value property. A p-harmonic function u is a viscosity solution to Δ p u = div(|∇u| p-2 ∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if and only if the expansion u(x) = α/2 {max/B e (x) u + min/B e (x) u} + β/|B e (x)| ∫B e (x) u dy + o(e 2 ) holds as e → 0 for x ∈ Ω in a weak sense, which we call the viscosity sense. Here the coefficients α, β are determined by α + β = 1 and α/β = (p - 2)/(N + 2).