We state a maximum principle for the gradient of the minima of integral functionals I(u) = integral(Omega) [f(delu) + g(u)]dx. on (u) over bar + 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.
Gradient maximum principle for minima
MARICONDA, CARLO;TREU, GIULIA
2002
Abstract
We state a maximum principle for the gradient of the minima of integral functionals I(u) = integral(Omega) [f(delu) + g(u)]dx. on (u) over bar + 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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