Now showing items 1-6 of 6
Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem [Article]
(National Academy of Sciences (United States), 2014)
In this paper, for both the sharp front surface quasi-geostrophic equation and the Muskat problem, we rule out the “splash singularity” blow-up scenario; in other words, we prove that the contours evolving from either of ...
New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory [Article]
A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller that the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control ...
Compactness properties of commutators of bilinear fractional integrals [Article]
Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, ...
Uncertainty principle estimates for vector fields [Article]
We derive weighted norm estimates for integral operators of potential type and for their related maximal operators. These operators are generalizations of the classical fractional integrals and fractional maximal functions. ...
On the Muskat problem: global in time results in 2D and 3D [Article]
(Johns Hopkins University Press, 2016-12)
This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an L2 maximum principle for the fluid interface. We also show global in time existence for strong ...
Concentration of the distance in finite dimensional normed spaces [Article]
(University College London, Faculty of Mathematical and Physical Sciences, Department of Mathematics, 1998-12)
We prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ∥x − y∥ is more than √2(1 − ε). As a consecuence, we obtain a result proved by Bourgain, using QS-descomposition, ...