Gradient Maximum Principle for Minima

C. Mariconda and G. Treu
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C. Mariconda: University of Padova
G. Treu: University of Padova

Journal of Optimization Theory and Applications, 2002, vol. 112, issue 1, No 9, 167-186

Abstract: 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.

Keywords: Comparison principle; gradient maximum principle; Lipschitz regularity; maximum principle (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1013052830852

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