论文标题
仿射$ p $ laplace方程的最少能源解决方案涉及亚临界和批判性非线性
Least energy solutions for affine $p$-Laplace equations involving subcritical and critical nonlinearities
论文作者
论文摘要
本文与涉及载体$ p $ p $ - laplace非局部运算符$Δ_p^{\ cal a} $的巷道和布雷兹·尼伦贝格有关的问题有关，这是在\ cite {hjm5}中引入的{ Lutwak，Yang和Zhang \ cite {lyz2}。我们对$ C^1 $最少能源类型的阳性$ C^1解决方案的存在和不存在。主要困难的一部分是由于缺乏$ {\ cal e} _ {p，ω} $以及比较$ {\ cal e} _ {p，ω}（u）
The paper is concerned with Lane-Emden and Brezis-Nirenberg problems involving the affine $p$-laplace nonlocal operator $Δ_p^{\cal A}$, which has been introduced in \cite{HJM5} driven by the affine $L^p$ energy ${\cal E}_{p,Ω}$ from convex geometry due to Lutwak, Yang and Zhang \cite{LYZ2}. We are particularly interested in the existence and nonexistence of positive $C^1$ solutions of least energy type. Part of the main difficulties are caused by the absence of convexity of ${\cal E}_{p,Ω}$ and by the comparison ${\cal E}_{p,Ω}(u) \leq \Vert u \Vert_{W^{1,p}_0(Ω)}$ generally strict.
