Quasilinear Lane-Emden equations with absorption and measure data
Quasilinear Lane-Emden equations with absorption and measure data
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DOI：
10.1016/j.matpur.2013.11.011
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发表时间：
2012-12
期刊：
影响因子：
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通讯作者：
Marie-Franccoise Bidaut-V'eron;Hung Nguyen Quoc;L. Véron
中科院分区：
文献类型：
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作者：
Marie-Franccoise Bidaut-V'eron;Hung Nguyen Quoc;L. Véron
当 g (x,.) 是非减函数且 μ 是测度时，我们研究方程 − Δ p u+ g (x, u)= μ 解的存在性。我们描述好的措施，即问题有重整化解决方案的措施。我们特别研究 g (x, u)=| 的情况x|− β|你| q− 1 u 和 g (x, u)= sgn (u)(e τ| u| λ− 1)。结果表明，如果测量相对于适当的洛伦兹-贝塞尔容量绝对连续，则该测量是好的。
We study the existence of solutions to the equation− Δ p u+ g (x, u)= μ when g (x,.) is a nondecreasing function and μ a measure. We characterize the good measures, ie the ones for which the problem has a renormalized solution. We study particularly the cases where g (x, u)=| x|− β| u| q− 1 u and g (x, u)= sgn (u)(e τ| u| λ− 1). The results state that a measure is good if it is absolutely continuous with respect to an appropriate Lorentz–Bessel capacities.