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Communications on Pure and Applied Mathematics, ISSN 0010-3640, 08/2014, Volume 67, Issue 8, pp. 1219 - 1262
For a family of second‐order elliptic operators with rapidly oscillating periodic coefficients, we study the asymptotic behavior of the Green and Neumann functions, using Dirichlet and Neumann correctors... 
MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | DIRICHLET PROBLEM | LIPSCHITZ-DOMAINS | DIVERGENCE FORM | EQUATION | SINGULAR-INTEGRALS | COMPACTNESS METHODS
Journal Article
Communications in nonlinear science & numerical simulation, ISSN 1007-5704, 2015, Volume 21, Issue 1-3, pp. 99 - 111
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2010, Volume 224, Issue 3, pp. 910 - 966
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 1, pp. 44 - 69
.... We study extensions of Newtonian Sobolev functions to the completion Xˆ of X and use them to obtain several results on X itself, in particular concerning minimal weak... 
Newtonian Sobolev space | Lebesgue point | Quasiminimizer | Noncomplete metric space | p-harmonic function | Poincaré inequality | QUASICONTINUITY | QUASIMINIMIZERS | LIPSCHITZ FUNCTIONS | POTENTIAL-THEORY | OPEN SETS | MATHEMATICS | QUASIOPEN | Poincare inequality | HARMONIC-FUNCTIONS
Journal Article
Acta mathematica, ISSN 0001-5962, 2011, Volume 207, Issue 2, pp. 375 - 389
.... In particular, we prove that every Lipschitz function is operator-Lipschitz in the Schatten–von Neumann ideals S α , 1 < α... 
Mathematics, general | Mathematics | Schatten–von Neumann ideals | Operator-Lipschitz functions | Schatten-von Neumann ideals | INTEGRALS | MATHEMATICS | CONTINUITY | SPACES | Perturbation theory | Norms | Errors | Syntax | Mathematical analysis | Linear operators
Journal Article
Journal of optimization theory and applications, ISSN 1573-2878, 2019, Volume 182, Issue 3, pp. 885 - 905
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 06/2019, Volume 349, pp. 1198 - 1233
..., where the observable variance is defined to be the supremum of the variance of 1-Lipschitz functions on the space... 
Observable variance | Concentration of measure | Lipschitz function | Isoperimetric profile | Metric measure space | METRIC-MEASURE-SPACES | INEQUALITIES | RICCI CURVATURE | MATHEMATICS | THEOREMS | SHARP | GEOMETRY | SURFACES
Journal Article
2014, De Gruyter studies in mathematics, ISBN 9783110281231, Volume 52., xiii, 449
Book
eBook
Advances in computational mathematics, ISSN 1572-9044, 2015, Volume 42, Issue 2, pp. 333 - 360
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2018, Volume 464, Issue 1, pp. 473 - 492
We study the Daugavet property in the space of Lipschitz functions Lip0(M) on a complete metric space M... 
Strongly exposed point | Daugavet property | Space of Lipschitz functions | Lipschitz-free space | Length space | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of functional analysis, ISSN 0022-1236, 2018, Volume 275, Issue 8, pp. 2015 - 2058
.... Second, we prove a square function bound for a single scale directional operator. As a corollary we give a new proof of part of a theorem of Katz on direction fields... 
Bi-Lipschitz maps | Littlewood–Paley diagonalization | Directional Hilbert transform | Directional square functions | MATHEMATICS | FIELDS | PLANE | HILBERT-TRANSFORMS | Littlewood-Paley diagonalization | SINGULAR-INTEGRALS | Mathematics - Classical Analysis and ODEs
Journal Article
2012, Annals of mathematics studies, ISBN 9780691153551, Volume no. 179, ix, 425
...-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces... 
Calculus of variations | Functional analysis | Banach spaces | Mathematics | Frechet spaces | Lipschitz spaces
Book
SIAM journal on optimization, ISSN 1095-7189, 2013, Volume 23, Issue 1, pp. 508 - 529
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2019, Volume 132, pp. 457 - 482
Given an arbitrary planar ∞-harmonic function u, for each α>0 we establish a quantitative Wloc1,2-estimate of |Du|α... 
Sobolev regularity | harmonic function | Absolute minimizer | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | infinity-harmonic function | MINIMIZATION PROBLEMS | LIPSCHITZ EXTENSIONS
Journal Article