Texts on Concepts – 4 – 9 November 2013 Uniqueness This is probably one of the most popular concepts in Calculus of Variations when we study solutions and their regularity, and especially in what concerns the Strong Maximum Principle. So, one of the strongest results we can obtain in variational calculus is uniqueness of solutions. If we find hypothesis which guarantee uniqueness it is a huge result and we can achieve great results regarding applications to industry, medicine and so on, based on this guarantee of uniqueness. And sometimes, within some specific results, we can even achieve uniqueness using very general hypothesis. In Performance Art, the concept of uniqueness is different, but I want to consider it in the same direction as in calculus of variations. That is, considering some specific problem, and presenting some solutions to that problem, we find ways to determine whether there is uniqueness or under which conditions we achieve uniqueness. When we consider the possibility of doing a performance, problems have several possibilities of solutions, and in general, as in calculus of variations, there is no unicity of solution, unless we impose some strong hypothesis. And the essence of my work is exactly to weaken hypothesis in order to establish uniqueness with almost no conditions. So, it is also the work done in performance. We define the possibilities, the way we deal with them, and we identify then the solutions. After that phase the main work is try to find uniqueness – to choose a path” – where we have the least assumptions possible, and so we need to drop some conditions, and to add others. In the end, even if we know that following others paths we would probably obtain other solutions and other performances, we know that the path we decided to take in is the strongest and also have the weakest solutions possible in the context of the specific problem.
Posted on: Sun, 10 Nov 2013 11:23:27 +0000
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