线性与半线性X-椭圆方程中系数相互作用的正则化效应
Regularizing effect of the interplay between coefficients in linear and semilinear $X$-elliptic equations
AI总结：
本文研究X-椭圆方程中零阶项系数a与数据f相互作用产生的正则化效应，证明Arcoya-Boccardo的Q-条件在f∈L^1(Ω)时足以保证解的存在性与有界性，并在更一般条件下证明线性问题有界解的存在性。
摘要：
我们研究由零阶项系数a与数据f之间的相互作用所产生的正则化效应，所考虑的问题为：在Ω中满足 -Lu + a(x)g(u) = f(x)，在∂Ω上满足u = 0，其中Ω⊆R^N是有界区域，L是由Lanconelli和Kogoj引入的X-椭圆算子。若f∈L^1(Ω)，我们证明Arcoya和Boccardo引入的Q-条件在X-椭圆算子框架下同样足以保证解的存在性和有界性。最后，我们在f与a之间更一般的条件下证明了线性问题有界解的存在性。
英文摘要：
We study the regularizing effect arising from the interaction between the coefficient \(a\) of the zero order term and the datum \(f\) in the problem $$ \left\lbrace \begin{array}{ll} -\mathcal{L}u + a(x) g(u) = f(x) \quad &\mbox{in} \;\; Ω, u = 0 \quad &\mbox{on} \;\; \partialΩ, \end{array} \right. $$ where $Ω\subseteq\mathbb{R}^N$ is a bounded domain and $\mathcal{L}$ is an $X$-elliptic operator introduced by Lanconelli and Kogoj. If $f \in L^1(Ω)$, we prove that the \(Q\)-condition introduced by Arcoya and Boccardo is sufficient to ensure the existence and boundedness of solutions in the framework of $X$-elliptic operators as well. Finally, we prove the existence of a bounded solution for linear problems under a more general condition between $f$ and $a$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
