Existence of a BV solution for a mean curvature equation
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Data
2021-10-25
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Resumo
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.
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Existence of solution, Functions of bounded variation, Geometric measure theory, Mean curvature equation
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Journal of Differential Equations, v. 299, p. 51-64.