The Euler equation for functionals with linear growth
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Abstract:
We give a first variation formula for functionals of the type $\int _\Omega {f(x,\mu )}$, where $f(x,p):\Omega \times {{\mathbf {R}}^k} \to {\mathbf {R}}$ is of linear growth in $p$ for large $|p|$ and $\mu$ is a ${{\mathbf {R}}^k}$-valued measure in $\Omega$. The Euler equation for the minima of various functionals defined on spaces of ${\text {BV}}$ functions is then studied.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 290 (1985), 483-501
- MSC: Primary 49A50; Secondary 26B05, 35D05
- DOI: https://doi.org/10.1090/S0002-9947-1985-0792808-4
- MathSciNet review: 792808