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The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
Harnack inequality second-order parabolic equations divergence-free drifts low regularity
2015/7/14
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity.While our previous work [IKR] considered the elliptic case, here we treat the more ch...
G-graded Castelnuovo Mumford Regularity
G-graded Castelnuovo Mumford Regularity Commutative Algebra Algebraic Geometry
2011/9/5
Abstract: We develop a general graded variant of Castelnuovo-Mumford regularity for modules over a commutative ring $R$ graded by a finitely generated abelian group $G$. With this aim, we establish a ...
Arens Regularity and Module Arens Regularity of Module Actions
Arens regularity Bilinear mappings Topological center Second dual
2011/1/20
In this paper, we extend some problems from Arens regularity and module Arens regularity of Banach algebras to module actions.
Multiplicity and regularity of periodic solutions for a class of degenerate semilinear wave equations
Multiplicity regularity of periodic solutions class of degenerate semilinear wave equations
2011/2/28
We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations:utt − uxx + |u|s−1u = f(x, t),for all s > 1. In particular we pro...
On the manifold structure of the set of unparameterized embeddings with low regularity
manifold structure unparameterized embeddings
2010/11/24
Given manifolds $M$ and $N$, with $M$ compact, we study the geometrical structure of the space of embeddings of $M$ into $N$, having less regularity than $\mathcal C^\infty$, quotiented by the group o...
We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suit...
Integral Menger curvature for sets of arbitrary dimension in $\mathbb{R}^n$. Part I: Uniform Ahlfors regularity
Integral Menger curvature math
2010/11/15
We propose the notion of integral Menger curvature for $m$-dimensional sets in $n$-dimensional Euclidean space and prove that finiteness of this quantity implies Ahlfors regularity with constant depe...
Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels
fully nonlinear integro-differential operators nonsymmetric positive kernels
2010/11/22
In this paper, we consider fully nonlinear integro-differential equations with possibly nonsymmetric kernels. We are able to find different versions of Alexandroff-Backelman-Pucci estimate correspondi...
Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains
Spatial Besov Regularity Partial Differential Equations Lipschitz Domains
2010/11/15
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential ...
Beurling-Fourier algebras, operator amenability and Arens regularity
locally compact groups Beurling algebras Beurling-Fourier algebras operator amenability operator weak amenability
2010/11/26
We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras.