| Abstract: |
| In this talk we focus on the boundary regularity of the solutions to Poisson-type problems with homogeneous boundary datum.
We discuss the geometric case of the Heisenberg group, where we fix the subLaplacian as the relevant (degenerate-elliptic) operator and the characteristic half-space as the (scale-invariant) domain. We show an intrinsic second order expansion at the only characteristic point of the boundary when the source term belongs to an appropriate weighted $L^\infty$ space. The technique we adopt is inspired by Caffarelli approach to Krylov`s boundary $C^{1,\alpha}$-estimate for uniformly elliptic operators in nondivergence form.
This is a joint work with F. Abedin. |
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