Variational problems related to the 1-Laplace operator

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Various problems in nature, technology and economy lead to a so called variational problem where a certain energy function has to be minimized under suitable constraints and the solution satisfies some associated differential equation. The methods for the treatment of such problems are mainly based on the differentiability of the involved functionals and operators. However, in the recent applications one is more and more confronted with situations where the usual assumptions concerning differentiability are not available. However, the study of such nondifferentiable problems is still in an early stage. The present project intends to contribute to this development by investigating current issues occuring in the context of the 1-Laplace operator that enjoys increasing interest for instance in image processing. The comprehensive experience of the applicant in the treatment of nondifferentiable problems in mechanics and geometry and, recently, also in the problems under consideration are certainly a solid foundation for successful investigations. The project aims to contribute to the treatment of a permanently growing class of problems in calculus, geometry, and applications, which will certainly gain significance in the near future, not only by the investigation of concrete problems but also by the development and establishment of methods.