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Gradient Maximum Principle for Minima

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Abstract

We state a maximum principle for the gradient of the minima of integral functionals

$$I(u) = \int_\Omega{f(\nabla u)}+ g(u)]dx,{\text{on }}\bar u + W_0^{1,1} (\Omega ),$$

just assuming that I is strictly convex. We do not require that f, g be smooth, nor that they satisfy growth conditions. As an application, we prove a Lipschitz regularity result for constrained minima.

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Authors and Affiliations

  1. Faculty of Engineering, University of Padova, Padova, Italy

    C. Mariconda (Associate Professor)

  2. Faculty of Statistical Sciences, University of Padova, Padova, Italy

    G. Treu (Associate Professor)

Authors
  1. C. Mariconda
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  2. G. Treu
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Mariconda, C., Treu, G. Gradient Maximum Principle for Minima. Journal of Optimization Theory and Applications 112, 167–186 (2002). https://doi.org/10.1023/A:1013052830852

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