The theory of curvature-dimension bounds for nonsmooth spaces has several motivations:
the study of functional and geometric inequalities in structures which arc very far from being …

We investigate well-posedness for martingale solutions of stochastic differential equations,
under low regularity assumptions on their coefficients, widely extending the results first …

We establish, in a rather general setting, an analogue of DiPerna–Lions theory on well-
posedness of flows of ODEs associated to Sobolev vector fields. Key results are a well …

New estimates for elliptic equations and Hodge type systems Page 1 J. Eur. Math. Soc. 9,
277–315 c European Mathematical Society 2007 Jean Bourgain · Haım Brezis New estimates …

New estimates for the Laplacian, the div–curl, and related Hodge systems Page 1 CR Acad. Sci.
Paris, Ser. I 338 (2004) 539–543 Partial Differential Equations New estimates for the Laplacian …

We study a class of nonlocal partial differential equations presenting a tensor-mobility, in
space, obtained asymptotically from nonlocal dynamics on localizing infinite graphs. Our …

In [7] Cheeger, proved that in every doubling metric measure space (X, ρ, µ) satisfying a
Poincaré inequality Lipschitz functions are di erentiable µ-almost everywhere. More …

We prove the equivalence of two seemingly very different ways of generalising
Rademacher's theorem to metric measure spaces. One such generalisation is based upon …

In this paper we deal with weak solutions to the Maxwell–Landau–Lifshitz equations and to
the Hall–Magneto–Hydrodynamic equations. First we prove that these solutions satisfy some …

For every finite measure μ μ on R^ n R n we define a decomposability bundle V (μ,\, ⋅) V
(μ,·) related to the decompositions of μ μ in terms of rectifiable one-dimensional measures …