Quasilinear elliptic equations with sub-natural growth terms in bounded domains
Quasilinear elliptic equations with sub-natural growth terms in bounded domains
复制标题
DOI：
10.1007/s00030-021-00724-5
复制
发表时间：
2020-05
期刊：
影响因子：
--
通讯作者：
Takanobu Hara
中科院分区：
文献类型：
--
作者：
Takanobu Hara
研究了-Δ p，wu= σ uq in Ω，u= 0 on Ω Ω的加权拟线性椭圆型微分方程在次自然增长情形0< q< p-1 0< q< p-1下正解的存在性，其中Ω Ω是R^nRn中的有界区域，Δ p，w Δ p，w是加权p-Laplacian，σ σ是Ω Ω上的非负（局部有限）Radon测度.我们给出了存在性问题的判据。为了证明这一点，我们研究了p-超调和函数的各种性质，特别是无穷测度Dirichlet问题的可解性。
We consider the existence of positive solutions to weighted quasilinear elliptic differential equations of the type-Δ p, wu= σ uq in Ω, u= 0 on∂ Ω in the sub-natural growth case 0< q< p-1 0< q< p-1, where Ω Ω is a bounded domain in R^ n R n, Δ _ p, w Δ p, w is a weighted p-Laplacian, and σ σ is a nonnegative (locally finite) Radon measure on Ω Ω. We give criteria for the existence problem. For the proof, we investigate various properties of p-superharmonic functions, especially the solvability of Dirichlet problems with infinite measure data.