论文标题
对非局部双相方程的有界弱解的自我改进不平等
Self-improving Inequalities for bounded weak solutions to nonlocal double phase equations
论文作者
论文摘要
我们证明，对于一类非线性非局部界面方程的有限弱解决方案，我们证明了较高的sobolev规则性。 The leading operator exhibits nonuniform growth, switching between two different fractional elliptic ``phases" that are determined by the zero set of a modulating coefficient. Solutions are shown to improve both in integrability and differentiability. These results apply to operators with rough kernels and modulating coefficients. To obtain these results we adapt a particular fractional version of the Gehring lemma developed by Kuusi, Mingione, and Sire in their工作``非局部自我改善特性''肛门。 PDE，8（1）：57--114，用于本手稿中正在研究的特定非线性设置。
We prove higher Sobolev regularity for bounded weak solutions to a class of nonlinear nonlocal integro-differential equations. The leading operator exhibits nonuniform growth, switching between two different fractional elliptic ``phases" that are determined by the zero set of a modulating coefficient. Solutions are shown to improve both in integrability and differentiability. These results apply to operators with rough kernels and modulating coefficients. To obtain these results we adapt a particular fractional version of the Gehring lemma developed by Kuusi, Mingione, and Sire in their work ``Nonlocal self-improving properties" Anal. PDE, 8(1):57--114 for the specific nonlinear setting under investigation in this manuscript.
