24 citations · 45 across the 22 of their papers we have counts for
24 papers
Fundamental solution for higher order homogeneous hypoelliptic operators structured on Hörmander vector fields
Stefano Biagi, Marco Bramanti
We introduce and study a new class of higher order differential operators defined on , which are built with Hörmander vector fields, homogeneous w.r.t. a family of…
Global Sobolev theory for Kolmogorov-Fokker-Planck operators with coefficients measurable in time and in space
Stefano Biagi, Marco Bramanti
We consider Kolmogorov-Fokker-Planck operators of the form with $\…
Global Sobolev regularity for nonvariational operators built with homogeneous Hörmander vector fields
Stefano Biagi, Marco Bramanti
We consider a class of nonvariational degenerate elliptic operators of the kind \[ Lu=\sum_{i,j=1}^{m}a_{ij}\left( x\right) X_{i}X_{j}u \] where $\left\{ a_{ij}\left( x\right) \rig…
KFP operators with coefficients measurable in time and Dini continuous in space
Stefano Biagi, Marco Bramanti, Bianca Stroffolini
We consider degenerate KFP operators \[ Lu=\sum_{i,j=1}^{m_{0}}a_{ij}(x,t)\partial_{x_{i}x_{j}}^{2}u+\sum_{k,j=1}^{N}b_{jk}x_{k}\partial_{x_{j}}u-\partial_{t}u\equiv\sum_{i,j=1}^{m…
Schauder estimates for Kolmogorov-Fokker-Planck operators with coefficients measurable in time and Hölder continuous in space
Stefano Biagi, Marco Bramanti
We consider degenerate Kolmogorov-Fokker-Planck operators $$ \mathcal{L}u=\sum_{i,j=1}^{q}a_{ij}(x,t)\partial_{x_{i}x_{j}}^{2}u+\sum_{k,j=1}^{N}b_{jk}x_{k}\partial_{x_{j}}u-\partia…
Non-divergence operators structured on homogeneous Hörmander vector fields: heat kernels and global Gaussian bounds
Stefano Biagi, Marco Bramanti
Let be a family of real smooth vector fields defined in , -homogeneous with respect to a nonisotropic family of dilations and satisfying Hörman…