Kolmogorov-Fokker-Planck equations: comparison principles near Lipschitz type boundaries (Q290566)

The authors prove several new results regarding the boundary behavior of non-negative solutions to the equation \(\mathcal Ku=0\) in \(\Omega\), where NEWLINE\[NEWLINE\mathcal K:=\sum_{i=1}^m\partial_{x_i}\partial_{x_i}+\sum_{i=1}^m x_i \partial_{y_i}-\partial_t,\quad (x,y,t)\in \mathbb R^m\times \mathbb R^m\times\mathbb RNEWLINE\]NEWLINE and \(\Omega\subset \mathbb R^{2m+1}\) is a bounded domain.NEWLINENEWLINEThe results obtained are established near the non-characteristic part of \(\partial\Omega\) for local \(\mathrm{Lip}_{\mathcal K}\)-domains \(\Omega\), where the latter is a class of local Lipschitz type domains adapted to the geometry of \(\mathcal K\). Applications to more general operators of Kolmogorov-Fokker-Planck type are also discussed.