Faithfulness of Top Local Cohomology Modules in Domains

We study the conditions under which the highest nonvanishing local cohomology module of a domain $R$ with support in an ideal $I$ is faithful over $R$, i.e., which guarantee that $H_I^c(R)$ is faithful, where $c$ is the cohomological dimension of $I$. In particular, we prove that this is true for the case of positive prime characteristic when $c$ is the number of generators of $I$.