Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2014 We give a positive answer to a question raised by Alberti in connection with a recent result by Brezis and Nguyen. We show the existence of currents associated with graphs of maps in trace spaces that have vanishing mean oscillation. The degree of such maps may be written in terms of these currents, of which we give some structure properties.
Emilio Acerbi, Domenico Mucci
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Homogeneous Herz spaces with variable exponents and regularity results [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2018 In this paper we deal with the second order divergence form operators $\mathcal{L}$ with coefficients satisfying the vanishing mean oscillation property and we prove some regularity results for a solution to $\mathcal{L}u=\mathrm{div}\, f$, where $f ...
Andrea Scapellato
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Parabolic equations with VMO coefficients in Morrey spaces [PDF]
Electronic Journal of Differential Equations, 2001 Global regularity in Morrey spaces is derived for the regular oblique derivative for linear uniformly parabolic operators. The principal coefficients of the operator are supposed to be discontinuous, belonging to Sarason's class of functions with ...
Lubomira G. Softova
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Regular oblique derivative problem in Morrey spaces [PDF]
Electronic Journal of Differential Equations, 2000 This article presents a study of the regular oblique derivative problem $$ displaylines{ sum_{i,j=1}^n a^{ij}(x) frac{partial^2 u }{partial x_ipartial x_j} =f(x) cr frac{partial u }{partial ell(x)}+ sigma(x) u = varphi(x),.
Dian K. Palagachev +2 more
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A decomposition of functions with vanishing mean oscillation [PDF]
, 2008 A function has vanishing mean oscillation (VMO) on R up(n) if its mean oscillation - the local average of its pointwise deviation from its mean value - both is uniformly bounded over all cubes within R up(n) and converges to zero with the volume of the cube.
Korey, Michael Brian
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Boundary partial Holder regularity for elliptic systems with non-standard growth [PDF]
Electronic Journal of Differential Equations, 2018 We investigate regular points on the boundaries of elliptic systems with non-standard growth, in particular, so-called Orlicz growth. A regular point on the boundary in this paper is a point for which a weak solution to a system is Holder continuous ...
Jihoon Ok
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Extension Theorems for Functions of Vanishing Mean Oscillation [PDF]
, 1987 A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in Rd converges to zero with the volume of the cubes.
Holden, Peter James
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Slowly Vanishing Mean Oscillations: Non-uniqueness of Blow-ups in a Two-phase Free Boundary Problem
Vietnam Journal of Mathematics, 2023 In Kenig and Toro's two-phase free boundary problem, one studies how the regularity of the Radon-Nikodym derivative $h= dω^-/dω^+$ of harmonic measures on complementary NTA domains controls the geometry of their common boundary. It is now known that $\log h \in C^{0,α}(\partial Ω)$ implies that pointwise the boundary has a unique blow-up, which is the ...
Matthew Badger +2 more
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Generalized Vanishing Mean Oscillation Spaces Associated with Divergence Form Elliptic Operators [PDF]
Integral Equations and Operator Theory, 2010 Integral Equations Operator Theory (to appear)
Jiang, Renjin, Yang, Dachun
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Two-dimensional magnetohydrodynamic turbulence in the limits of infinite and vanishing magnetic Prandtl number [PDF]
, 2013 LAKB was supported by an EPSRC post-graduate studentship.We study both theoretically and numerically two-dimensional magnetohydrodynamic turbulence at infinite and zero magnetic Prandtl number $Pm$ (and the limits thereof), with an emphasis on solution ...
Tran, Chuong Van +2 more
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