Options
A Lewy-Stampacchia estimate for variational inequalities in the Heisenberg group
Pinamonti, Andrea
Valdinoci, Enrico
2013
Abstract
We consider an obstacle problem in the
Heisenberg group framework, and we prove that the
operator on the obstacle
bounds pointwise the operator on the solution.
More explicitly,
if~$\bar u$ minimizes
the functional
$$ \int_\Omega |\nabla_{\H^n}u|^2$$
among the functions with prescribed Dirichlet boundary
condition that stay below a smooth obstacle~$\psi$, then
$$
0\leq \Delta_{\H^n} \bar u\leq \Big(\Delta_{\H^n}\psi\Big)^{+}.
$$
Moreover, we discuss how it could be possible to generalize the
previous
bound to a quasilinear setting once some regularity issues for the
equation
$$
\div_{\H^n}\Big(|\nabla_{\H^n}u|^{p-2}\nabla_{\H^n}u\Big)=f
$$
are satisfied.}
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
45 (2013)
Publisher
EUT Edizioni Università di Trieste
Source
Andrea Pinamonti and Enrico Valdinoci, "A Lewy-Stampacchia estimate for variational inequalities in the Heisenberg group", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 45 (2013), pp. 23–45.
Languages
en
File(s)