Estimate of the pressure when its gradient is the divergence of a measure. Applications
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1066-1087.

In this paper, a W -1,N ' estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on N , or on a regular bounded open set of  N . The proof is based partially on the Strauss inequality [Strauss, Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973) 207-214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc. 9 (2007) 277-315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and to prove an existence result for the stationary Navier-Stokes equation when the viscosity tensor is only in L1.

DOI : 10.1051/cocv/2010037
Classification : 35Q30, 35Q35, 35A08
Mots clés : pressure, Navier-Stokes equation, div-curl, measure data, fundamental solution
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     title = {Estimate of the pressure when its gradient is the divergence of a measure. {Applications}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Briane, Marc; Casado-Díaz, Juan. Estimate of the pressure when its gradient is the divergence of a measure. Applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1066-1087. doi : 10.1051/cocv/2010037. http://www.numdam.org/articles/10.1051/cocv/2010037/

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