论文标题
Hölder的连续性和Heisenberg组非线性分数方程的界限估计值
Hölder continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group
论文作者
论文摘要
我们将庆祝的de Giorgi-nash-Moser理论扩展到了由非本地，可能是堕落的，不差异的操作员驱动的广泛的非线性方程式，其模型是分数$ p $ -laplacian操作员在Heisenberg-weyl Group $ \ Mathbb $ \ Mathbb {H}^n $上。除其他结果外，我们证明，通过建立一般估计值作为尾巴和对数型估计值的分数caccioppoli-type估计值，我们证明了此类问题的薄弱解决方案是有限的，并且连续Hölder连续。
We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional $p$-Laplacian operator on the Heisenberg-Weyl group $\mathbb{H}^n$. Amongst other results, we prove that the weak solutions to such a class of problems are bounded and Hölder continuous, by also establishing general estimates as fractional Caccioppoli-type estimates with tail and logarithmic-type estimates.
