On the Dirichlet problem for nonlinear degenerate elliptic equations and applications to optimal control.
Bardi, M., Bottacin, S. (1998)
Rendiconti del Seminario Matematico
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On the Dirichlet problem for nonlinear degenerate elliptic equations and applications to optimal control.
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In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, (1992)...