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Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane, Juan Casado-Díaz (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane, Juan Casado-Díaz (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Explicit fundamental solutions of some second order differential operators on Heisenberg groups

Isolda Cardoso, Linda Saal (2012)

Colloquium Mathematicae

Let p,q,n be natural numbers such that p+q = n. Let be either ℂ, the complex numbers field, or ℍ, the quaternionic division algebra. We consider the Heisenberg group N(p,q,) defined ⁿ × ℑ , with group law given by (v,ζ)(v’,ζ’) = (v + v’, ζ + ζ’- 1/2 ℑ B(v,v’)), where B ( v , w ) = j = 1 p v j w j ¯ - j = p + 1 n v j w j ¯ . Let U(p,q,) be the group of n × n matrices with coefficients in that leave the form B invariant. We compute explicit fundamental solutions of some second order differential operators on N(p,q,) which are canonically associated to...

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