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Existence and Lipschitz regularity for minima

Author(s): Carlo Mariconda; Giulia Treu
Journal: Proc. Amer. Math. Soc. 130 (2002), 395-404.
MSC (2000): Primary 49J52, 49J99, 49K30, 49N60
Posted: September 19, 2001
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Abstract: We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional

\begin{displaymath}I(u)=\int _{\Omega }L(x,u,\nabla u)\,dx \end{displaymath}

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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Additional Information:

Carlo Mariconda
Affiliation: Dipartimento di Matematica pura e applicata, Università di Padova, 7 via Belzoni, I-35131 Padova, Italy
Email: maricond@math.unipd.it

Giulia Treu
Affiliation: Dipartimento di Matematica pura e applicata, Università di Padova, 7 via Belzoni, I-35131 Padova, Italy
Email: treu@math.unipd.it

DOI: 10.1090/S0002-9939-01-06370-5
PII: S 0002-9939(01)06370-5
Keywords: Barrier, Euler equation, existence of minima, Lavrentiev, Lipschitz regularity
Received by editor(s): May 20, 2000
Posted: September 19, 2001
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2001, American Mathematical Society

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