Accepted Paper

Inserted: 12 jul 2012
Last Updated: 12 jul 2012

Journal: Adv.Calc. Var
Year: 2012

Abstract:

In the present paper we consider the Dirichlet problem associated with a nonlinear singular elliptic equation, whose differential operator arises in the level set formulation of the inverse mean curvature flow; namely, we study $$ - \div \left(\frac{Du}{\vert Du \vert} \right) + \vert Du \vert = f\,. $$ We introduce a suitable concept of weak solution, for which we prove existence and uniqueness of the homogeneous Dirichlet problem in a bounded open set of $\R^N$ for data $f$ belonging to suitable Lebesgue spaces. Moreover, examples of explicit solutions are shown.

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