33 research outputs found
Continuous solutions for divergence-type equations associated to elliptic systems of complex vector fields
In this paper, we characterize all the distributions
such that there exists a continuous weak solution
(with ) to the divergence-type equation
where
is an elliptic system of linearly
independent vector fields with smooth complex coefficients defined on . In case where is the usual gradient
field on , we recover the classical result for the divergence
equation proved by T. De Pauw and W. Pfeffer
Averaging on n-dimensional rectangles
In this work we investigate families of translation invariant differentiation bases B of rectangles in Rn, for which L log^(n−1) L(R^n) is the largest Orlicz space that B differentiates. In particular, we improve on techniques developed by Stokolos in [11] and [13] (see the attached file)
AVERAGING ON n-DIMENSIONAL RECTANGLES
In this work we investigate families of translation invariant differentiation bases B of rectangles in R n , for which L log n−1 L(R n) is the largest Orlicz space that B differentiates. In particular, we improve on techniques developed by A. Stokolos in [7] and [9]
REMOVABLE SINGULARITIES FOR div v = f IN WEIGHTED LEBESGUE SPACES
International audienceLet be apositive weight. Assuming that a doubling condition and an Poincar\'e inequality on balls for the measure , as well as a growth condition on , we prove that the compact subsets of which are removable for the distributional divergence in are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for , , in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author
Differentiating Orlicz spaces with rare bases of rectangles
In the current paper, we study how the speed of convergence of a sequence of
angles decreasing to zero influences the possibility of constructing a rare
differentiation basis of rectangles in the plane, one side of which makes with
the horizontal axis an angle belonging to the given sequence, that
differentiates precisely a fixed Orlicz space
Removable singularities for the equation div v = 0
A compact subset S of R^N is removable for the equation div v = 0 if every bounded Borel vector field whose distributional divergence vanishes outside S, has a zero distributional divergence in the whole R^N. Here we establish that a compact subset of R^N is removable for the equation div v = 0 if and only if its (N−1)-dimensional Hausdorff measure vanishes