REGULARITY OF EXTREMAL SOLUTIONS OF A LIOUVILLE SYSTEM

OLIVIER GOUBET

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REGULARITY OF EXTREMAL SOLUTIONS OF A LIOUVILLE SYSTEM

机译：Liouville系统极值解决方案的规律性

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Let Ω⊂ R~n be a bounded smooth open set. We prove that the extremal solution of the system -Δu = μe~(θu+(1-θ)v), -Δv = λe(θv+(1-θ)u) in Ω, with u = v = 0 on ∂Ω, θ in [0, 1] and μ; λ≥ 0 are smooth if n≤ 9.

机译：让ω⊂r〜n是有界的平滑开放式集合。我们证明了系统-ΔU=μe〜（θu+（1-θ）v），-Δv=λe（θv+（1-θ）u）的极值解，u = v = 0on≥ω， θ在[0,1]和μ;如果n≤9，则λ≥0是光滑的。

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《Discrete and continuous dynamical systems▼hSeries S》 |2019年第2期|339-345|共7页
作者
OLIVIER GOUBET;
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作者单位

LAMFA UMR CNRS 7352 Universite de Picardie Jules Verne 33 rue St Leu 80039 Amiens Cedex France;

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正文语种 eng
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关键词
Regularity; Liouville system; extremal solution;

机译：规律性;刘维尔系统;极值解决方案;

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1. LIOUVILLE TYPE RESULTS AND REGULARITY OF THE EXTREMAL SOLUTIONS OF BIHARMONIC EQUATION WITH NEGATIVE EXPONENTS [J] . Zongming Guo, Juncheng Wei Discrete and continuous dynamical systems . 2014,第6期

机译：具有负指数的双线性方程的Liouville型结果和极值解的正则性
2. ON THE REGULARITY AND PARTIAL REGULARITY OF EXTREMAL SOLUTIONS OF A LANE EMDEN SYSTEM [J] . Hajlaoui Hatem Proceedings of the American Mathematical Society . 2019,第5期

机译：关于车辆欧登系统极值解决方案的规律性和部分规律
3. Extremal solutions for Emphasis Type="Italic"p/Emphasis-Laplacian fractional differential systems involving the Riemann-Liouville integral boundary conditions [J] . Ying He Advances in Difference Equations . 2018,第1期

机译：涉及Riemann-Liouville积分边界条件的 p -Laplacian分数阶微分系统的极值解
4. Regular Sturm-Liouville Problem with Riemann-Liouville Derivatives of Order in (1,2): Discrete Spectrum, Solutions and Applications [C] . Malgorzata Klimek, Marek Blasik Conference on non-integer order calculus and its applications . 2015

机译：（1,2）中具有阶Riemann-Liouville导数的正则Sturm-Liouville问题：离散谱，解和应用
5. Solutions for semilinear parabolic equations in L^P and Regularity of Weak Solutions of the Navier-Stokes System利用統計を見る [D] . Giga Yoshikazu 1985

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6. Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems [O] . Qing Zhao, Shuhong Chen -1

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7. Regularity of extremal solutions of a Liouville system [O] . Olivier Goubet 2019

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8. On Extremal Solutions of Sturm-Liouville Inverse Problems [R] . Sabatier, P. C. 1979

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REGULARITY OF EXTREMAL SOLUTIONS OF A LIOUVILLE SYSTEM

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