| Abstrakt: |
Abstract: We study regularity results for solutions $u\in H W^{1,p}(\Omega)$ to the obstacle problem int_{\Omega} \mathcal{A}(x, \nabla_{\mathbb H} u)\nabla_{\mathbb H}(v-u) d x \geq0 \quad\forall v\in\mathcal K_{\psi,u}(\Omega)such that $u\geq\psi$ a.e. in $\Omega$, where $\mathcal K_{\psi,u}(\Omega)= \{v\in HW^{1,p}(\Omega) v-u\in HW_0^{1,p}(\Omega) v\geq\psi \text a.e. in \Omega\}$, in Heisenberg groups $\mathbb H^n$. In particular, we obtain weak differentiability in the $T$-direction and horizontal estimates of Calderon-Zygmund type, i.e. aligned T\psi\in HW^{1,p}_ loc(\Omega)&\Rightarrow Tu\in L^p_ loc(\Omega), $|\nabla_{\mathbb H}\psi|^p\in L^q_ loc(\Omega)&\Rightarrow|\nabla_{\mathbb H} u|^p \in L^q_ loc(\Omega),where $21$. |
