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 $L$.References
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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
- Received by editor(s): May 20, 2000
- Published electronically: September 19, 2001
- Communicated by: David S. Tartakoff
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 395-404
- MSC (2000): Primary 49J52, 49J99, 49K30, 49N60
- DOI: https://doi.org/10.1090/S0002-9939-01-06370-5
- MathSciNet review: 1862118