Year: 2022
Type: preprint
Abstract: We study existence and structure of solutions to the Dirichlet and Neumann boundary problems associated with minimizers of the functional $I(u)=\int_Ω (ϕ(x, D u + F)+Hu) \, dx$, where $ϕ(x, ξ)$, among other properties, is convex and homogeneous of degree $1$ with respect to $ξ$. We show that there exists an underlying vector field $N$ that characterizes the existence and structure of all minimizers. We also investigate existence of solutions under the barrier condition on $\partial Ω$. The results in this paper generalize and unify many results in the literature about existence of minimizers of least gradient problems and $P-$area minimizing surfaces.
Source: arXiv (Cornell University)
Authors: Moradifam, Amir, Rowell, Alexander
Institution: University of California, Riverside
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4310926679