A comparison principle and the Lipschitz continuity for minimizers (Q2768072)
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scientific article; zbMATH DE number 1698962
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A comparison principle and the Lipschitz continuity for minimizers |
scientific article; zbMATH DE number 1698962 |
Statements
21 May 2003
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Lipschitz regularity of minimizers
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Euler equation
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bounded slope condition
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A comparison principle and the Lipschitz continuity for minimizers (English)
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The authors state some results (with only sketch of proofs) on existence and Lipschitz regularity of minimizers of the functional NEWLINE\[NEWLINE \int_\Omega L(x,u,\nabla u)dx, \qquad u-\bar u\in W^{1,q}_0(\Omega),\quad 1\leq q\leq \infty , NEWLINE\]NEWLINE for a class of integrands \(L(x,z,p)=f(p)+g(x,u)\), convex in \((z,p)\) and data \(\bar u\) satisfying the bounded slope condition.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00020].
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