论文标题
通过分数最大运算符对非均匀非线性椭圆方程的全局洛伦兹估计
Global Lorentz estimates for non-uniformly nonlinear elliptic equations via fractional maximal operators
论文作者
论文摘要
本文是对非线性椭圆方程的规则性理论研究的贡献。本文的目的是建立一些以分歧形式的非均匀椭圆形的全球估计值\ begin {align*} - \ mathrm {div}（| \ nabla u |^{p-2} \ nabla u + a（x） \ Mathrm {div}（| \ Mathbf {f} |^{p-2} \ MathBf {f} + a（x）| \ Mathbf {f} |^{q-2} \ -Mathbf {f}），\ end end {align {align {align {align*}，从而出现了double double fape fartial functional functional functional functional functial functial functial functional functional functional functional functional函数。特别是，主要结果提供了分布解决方案的规律性估计，从最大和最大运算符方面。这项工作通过处理Lorentz空间中的全局估计值来扩展\ cite {Comin2016，byun2017cava}。这项工作还扩展了我们最近的结果\ cite {pnjde}，该结果使用截止分数最大运算符致力于新的椭圆方程的新估计值。为了将来的研究，本文开发的方法允许在其他空间框架中对非均匀非线性椭圆方程的分布解决方案进行全球估计。
This paper is a contribution to the study of regularity theory for nonlinear elliptic equations. The aim of this paper is to establish some global estimates for non-uniformly elliptic in divergence form as follows \begin{align*} -\mathrm{div}(|\nabla u|^{p-2}\nabla u + a(x)|\nabla u|^{q-2}\nabla u) = - \mathrm{div}(|\mathbf{F}|^{p-2}\mathbf{F} + a(x)|\mathbf{F}|^{q-2}\mathbf{F}), \end{align*} that arises from double phase functional problems. In particular, the main results provide the regularity estimates for the distributional solutions in terms of maximal and fractional maximal operators. This work extends that of \cite{CoMin2016,Byun2017Cava} by dealing with the global estimates in Lorentz spaces. This work also extends our recent result in \cite{PNJDE}, which is devoted to the new estimates of divergence elliptic equations using cut-off fractional maximal operators. For future research, the approach developed in this paper allows to attain global estimates of distributional solutions to non-uniformly nonlinear elliptic equations in the framework of other spaces.
