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Zap. Nauchn. Sem. POMI, 2013, Volume 411, Pages 63–84 (Mi znsl5632)  

Some results on Sobolev spaces with respect to a measure and applications to a new transport problem

J. Louet

Department de Mathématique, Bât. 425, Faculté des Sciences, Université Paris-Sud 11, F-91405 Orsay cedex, France

Abstract: We recall some known and present several new results about Sobolev spaces defined with respect to a measure $\mu$, in particular a precise pointwise description of the tangent space to $\mu$ in dimension 1. This allows to obtain an interesting, original compactness result which stays open in $\mathbb R^d$, $d>1$, and can be applied to a new transport problem, with gradient penalization.

Key words and phrases: weighted Sobolev spaces, tangent space to a measure, optimal transport, elasticity.

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English version:
Journal of Mathematical Sciences (New York), 2014, 196:2, 152–164

Bibliographic databases:
UDC: 517.972
Received: 28.02.2013
Language:

Citation: J. Louet, “Some results on Sobolev spaces with respect to a measure and applications to a new transport problem”, Representation theory, dynamical systems, combinatorial methods. Part XXII, Zap. Nauchn. Sem. POMI, 411, POMI, St. Petersburg, 2013, 63–84; J. Math. Sci. (N. Y.), 196:2 (2014), 152–164

Citation in format AMSBIB
\Bibitem{Lou13}
\by J.~Louet
\paper Some results on Sobolev spaces with respect to a~measure and applications to a~new transport problem
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXII
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 411
\pages 63--84
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5632}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3048269}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 196
\issue 2
\pages 152--164
\crossref{https://doi.org/10.1007/s10958-013-1647-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84897037990}


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