M. Bramanti

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math.AP2026

Fundamental solution for higher order homogeneous hypoelliptic operators structured on HÃ¶rmander vector fields

Stefano Biagi, Marco Bramanti

We introduce and study a new class of higher order differential operators defined on $R^{n}$ , which are built with HÃ¶rmander vector fields, homogeneous w.r.t. a family of…

math.AP2025

Global Sobolev theory for Kolmogorov-Fokker-Planck operators with coefficients measurable in time and $V M O$ in space

Stefano Biagi, Marco Bramanti

We consider Kolmogorov-Fokker-Planck operators of the form $L u = i, j = 1 \sum q a_{ij} (x, t) u_{x_{i} x_{j}} + k, j = 1 \sum N b_{j k} x_{k} u_{x_{j}} - \partial_{t} u,$ with $\…

math.AP2024

Global Sobolev regularity for nonvariational operators built with homogeneous HÃ¶rmander 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…

Fundamental solution for higher order homogeneous hypoelliptic operators structured on HÃ¶rmander vector fields

Global Sobolev theory for Kolmogorov-Fokker-Planck operators with coefficients measurable in time and VMO in space

Global Sobolev regularity for nonvariational operators built with homogeneous HÃ¶rmander vector fields

Global Sobolev theory for Kolmogorov-Fokker-Planck operators with coefficients measurable in time and $V M O$ in space