Abstract
We study existence of minimisers to the least gradient problem on a strictly convex domain in two settings. On a bounded domain, we allow the boundary data to be discontinuous and prove existence of minimisers in terms of the Hausdorff measure of the discontinuity set. Later, we allow the domain to be unbounded, prove existence of minimisers and study their properties in terms of the regularity of boundary data and the shape of the domain.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have