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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Euler equation for functionals with linear growth


Author: Gabriele Anzellotti
Journal: Trans. Amer. Math. Soc. 290 (1985), 483-501
MSC: Primary 49A50; Secondary 26B05, 35D05
MathSciNet review: 792808
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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 $ \vert p\vert$ 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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0792808-4
PII: S 0002-9947(1985)0792808-4
Article copyright: © Copyright 1985 American Mathematical Society