论文标题
非线性非本地抛物线$ p $ - 拉普拉斯方程
Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic $p$-Laplace equation
论文作者
论文摘要
我们建立了对双线非线性抛物线分数$ p $ laplace方程的弱亚物质估算的局部界限估计。我们的论点依赖于De Giorgi方法的能量估计和抛物线非本地版本。此外，通过新的代数不平等，我们表明积极的弱超溶液满足了反向Hölder的不平等。最后，我们还证明了对对数衰减估计值的积极超溶液。
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 Hölder inequality. Finally, we also prove a logarithmic decay estimate for positive supersolutions.
