1,721,013 research outputs found
On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations
No full textA Note on the Dimension of the Singular Set In Free Interface Problems
No full textThe aim of this note is to investigate the size of the singular set of a general class of free interface problems. We show porosity of the singular set, obtaining as a corollary that both its Hausdorff and Minkowski dimensions are strictly smaller than n−1
W^{2,1}- regularity for solutions of the Monge-Ampere equation
No full textIn this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, with right hand side bounded away from zero and infinity, is W2,1loc. This is obtained by showing higher integrability a-priori estimates for D2u, namely D2u∈LlogkL for any k∈N
An excess-decay result for a class of degenerate elliptic equations
No full textISSN:1937-1632ISSN:1937-1179ISSN:1937-117
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation
No full textCombining rearrangement techniques with Gromov’s proof (via optimal mass transportation) of the 1-Sobolev inequality, we prove a sharp quantitative version of the anisotropic Sobolev inequality on BV(Rn). We also deduce, as a corollary of this result, a sharp stability estimate for the anisotropic 1-log-Sobolev inequality
On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna–Lions
No full textAbstractIn this paper we extend the DiPerna–Lions theory of flows associated to Sobolev vector fields to the case of Cameron–Martin-valued vector fields in Wiener spaces E having a Sobolev regularity. The proof is based on the analysis of the continuity equation in E, and on uniform (Gaussian) commutator estimates in finite-dimensional spaces
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces
No full textHigher Integrability for Minimizers of the Mumford-Shah Functional
No full textWe prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi (Free discontinuity problems in calculus of variations. Frontiers in pure and applied mathematics, North-Holland, Amsterdam, pp 55-62, 1991). © 2014 Springer-Verlag Berlin Heidelberg
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