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- W2963692747 abstract "In a cylinder $$D_T = Omega times (0,T)$$ , where $$Omega subset mathbb {R}^{n}$$ , we examine the relation between the L-caloric measure, $$mathrm{d}omega ^{(x,t)}$$ , where L is the heat operator associated with a system of vector fields of Hörmander type, and the measure $$mathrm{d}sigma _Xtimes mathrm{d}t$$ , where $$mathrm{d}sigma _X$$ is the intrinsic X-perimeter measure. The latter constitutes the appropriate replacement for the standard surface measure on the boundary and plays a central role in sub-Riemannian geometric measure theory. Under suitable assumptions on the domain $$Omega $$ we establish the mutual absolute continuity of $$mathrm{d}omega ^{(x,t)}$$ and $$mathrm{d}sigma _Xtimes mathrm{d}t$$ . We also derive the solvability of the initial-Dirichlet problem for L with boundary data in appropriate $$ L^p$$ spaces, for every $$p>1$$ ." @default.
- W2963692747 created "2019-07-30" @default.
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- W2963692747 date "2017-05-25" @default.
- W2963692747 modified "2023-10-06" @default.
- W2963692747 title "Estimates of the Green function and the initial-Dirichlet problem for the heat equation in sub-Riemannian spaces" @default.
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- W2963692747 doi "https://doi.org/10.1007/s10231-017-0669-9" @default.
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