Existence of a BV solution for a mean curvature equation - Pimenta, Marcos T.O. [UNESP]; Montenegro, Marcelo (Elsevier, 2021)
We prove the existence of a bounded variation solution for a quasilinear elliptic problem involving the mean curvature operator and a sublinear nonlinearity. We obtain such a solution as the limit of the solutions of another quasilinear elliptic problem involving a parameter p>1 as p→1+. The analysis requires estimates independent on p, as well as a precise version of the weak Euler-Lagrange equation satisfied by the solution.
Keywords: Existence of solution; Functions of bounded variation; Geometric measure theory; Mean curvature equation