| 平面上拟线性偏微分方程组弱解的有界性 |
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| 引用本文： | 曾岳生,简怀玉. 平面上拟线性偏微分方程组弱解的有界性[J]. 怀化学院学报, 1992, 0(5) |
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| 作者姓名： | 曾岳生 简怀玉 |
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| 作者单位： | 怀化师专数学系(曾岳生)，怀化师专数学系(简怀玉) |
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| 摘 要： | 本文假定通常的椭圆条件仅在无穷远处成立,证明了平面上一类二阶拟线性偏微分方程组弱解是有界的。
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| 关 键 词： | 拟线性偏微组 椭圆条件 blow up技巧 |
Boundedness for Weak Solutions of Certain Qrosilinear Partial Differential Systems on Plane |
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| Zeng Yuesheng Jian Huaiyu. Boundedness for Weak Solutions of Certain Qrosilinear Partial Differential Systems on Plane[J]. Journal of Huaihua University, 1992, 0(5) |
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| Authors: | Zeng Yuesheng Jian Huaiyu |
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| Affiliation: | Department of Mathematics. |
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| Abstract: | Suppose Ω(?)R2 is an open set, and U∈H1(Ω, RN)satisfying (?)A11αβ(x, u)D βu1DαΦ1dx=(?)B11β(x, u)Dβu1Φ1dx, ∨Φ∈H01(Ω, RN)in which A11αβ(x, q), B11β(x, q)are bounded inΩ×RN satisfying(1) lim(?)|B11β(x,q)|=0 and lim(?)|A11αβ(x,q)=a11αβ|=0 hold uniformly for x∈Ω,with constants a11αβ satisfying a11αβξu1ξβ1≥λ|ξ|2 for some λ>0 and all ξ;(2) A11αβ(x,q1)-A11αβ(x,q2)|2 ≤W1(|q1-q2)|2), |B11αβ(x,q1)-B11β(x,q2)|2≤W2(|q1-q2|2)and |B11αβ(x,q1)-B11β(x,q2)|2≤W2(|q1-q2|2),wint Wk(·) beign bounded and satisfying Wk (λt)≤λ1wk(t) for some α,α0>0 and all 0<λ≤α0. Then in this paper we have proved u∈Lloc∞(Ω,RN). |
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| Keywords: | Quasilinear Partial Differential Systems Elliptic Condition. |
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