Gradient Maximum Principle for Minima |
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| Authors: | C Mariconda G Treu |
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| Institution: | (1) Faculty of Engineering, University of Padova, Padova, Italy;(2) Faculty of Statistical Sciences, University of Padova, Padova, Italy |
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| Abstract: | We state a maximum principle for the gradient of the minima of integral functionals
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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| Keywords: | Comparison principle gradient maximum principle Lipschitz regularity maximum principle |
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![$$I(u) = \int_\Omega{f(\nabla u)}+ g(u)]dx,{\text{on }}\bar u + W_0^{1,1} (\Omega ),$$](/content/n267041w49616282/10957_2004_Article_360922_TeX2GIFEqu1.gif)