Some local properties of subsolution and supersolutions for a doubly nonlinear nonlocal p-Laplace equation
Some local properties of subsolution and supersolutions for a doubly nonlinear nonlocal p-Laplace equation
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DOI：
10.1007/s10231-021-01177-4
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发表时间：
2021-11-15
影响因子：
1
通讯作者：
Kinnunen, Juha
中科院分区：
文献类型：
--
作者：
Banerjee, Agnid;Garain, Prashanta;Kinnunen, Juha
我们为双非线性抛物型分数 p-拉普拉斯方程的弱子解建立了局部有界估计。我们的论点依赖于能量估计和德乔治方法的抛物线非局部版本。此外，通过一个新的代数不等式，我们证明了正弱超解满足逆霍尔德不等式。最后，我们还证明了正超解的对数衰减估计。
We establish a local boundedness estimate for weak subsolutions to a doubly nonlinear parabolic fractional p-Laplace equation. Our argument relies on energy estimates and a parabolic nonlocal version of De Giorgi's method. Furthermore, by means of a new algebraic inequality, we show that positive weak supersolutions satisfy a reverse Holder inequality. Finally, we also prove a logarithmic decay estimate for positive supersolutions.