145 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)
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
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]
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
Hausdorff dimension of removable sets for elliptic and canceling homogeneous differential operators in the class of bounded functions
In this note we give an upper bound on the Hausdorff dimension of removable
setsfor elliptic and canceling homogeneous differential operators with constant
coefficients in the class of bounded functions, using a simple extension of
Frostman's lemma in Euclidean space with an additional power decay
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