| Autor: |
Behr, Florian, Dolzmann, Georg |
| Předmět: |
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| Zdroj: |
PAMM: Proceedings in Applied Mathematics & Mechanics; Dec2024, Vol. 24 Issue 4, p1-7, 7p |
| Abstrakt: |
Relaxed variational problems in the scalar case involving functions f:Rd→R$f: \mathbb {R}^d\rightarrow \mathbb {R}$ are frequently characterized by the convex envelope fc:Rd→R$f^c: \mathbb {R}^d\rightarrow \mathbb {R}$ of the energy density f$f$. For functions f$f$ with superlinear growth and Lipschitz continuous gradient, a formula for fc$f^c$ is presented in an open neighborhood Ω$\Omega$ of any maximal phase simplex provided that f$f$ is C1,1$C^{1,1}$ and strictly convex close to the vertices of the phase simplex. This formula involves a carefully chosen parameterization of Ω$\Omega$ which identifies those subsets in Ω$\Omega$ in which fc$f^c$ may be written as a convex combination of a prescribed number of function values. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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