Existence and Lipschitz regularity for minima

Mariconda, Carlo; Treu, Giulia

doi:10.1090/S0002-9939-01-06370-5

Existence and Lipschitz regularity for minima
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by Carlo Mariconda and Giulia Treu PDF

Proc. Amer. Math. Soc. 130 (2002), 395-404 Request permission

Abstract:

We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional \[ I(u)=\int _{\Omega }L(x,u,\nabla u) dx \] on $\bar u+W^{1,q}_{0}(\Omega )$ ($1\le q\le +\infty$) for a class of integrands $L(x,z,p)=f(p)+g(x,z)$ that are convex in $(z,p)$ and for boundary data satisfying some barrier conditions. We do not impose regularity or growth assumptions on $L$.

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