退化弱拟正则映射的Caccioppoli型不等式

得到退化弱拟正则映射的Caccioppoli不等式,这个不等式蕴涵其自我提高的正则性.     

Analytic Hypoellipticity at Non-Symplectic Poisson-Treves Strata for Certain Sums of Squares of Vector Fields

We consider an operator P which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form σ is not constant on Char P. Moreover the Hamilton foliation of the non-symplectic stratum of the Poisson-Treves stratification for P consists of closed curves in a ring-shaped open set around the origin. We prove that then P is analytic hypoelliptic on that open set. And we note explicitly that the local Gevrey hypoellipticity for P is G ^k+1 and that this is sharp.      

Optimal global regularity for minimal graphs over convex domains in hyperbolic space

We use the concept of the inside-(a, η, h) domain to construct a subsolution to the Dirichlet problem for minimal graphs over convex domains in hyperbolic space. As an application, we prove that the Hölder exponent \max \{1/a,1/(n+1)\} for the problem is optimal for any a\in [2,+\infty ].     

A Remark on the Sobolev Regularity of Classical Solutions to Uniformly Parabolic Equations

We prove that C^2+α,1+α/2 (Q?) solutions of problem (1.6) below are in a subspace H_c^m+2(Q) of H^{m+2,(m+2)/2(Q)} for all m ∈ ?, if f and the coefficients are in H_c^m(Q)∪C^α,α/2 (Q?). We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below.     

Solutions to two problems of G. J. Wang

The problem as to whether the sub-T₀ separation and complete regularity are invariant under homeomorphism is answered negatively. And, the problem of multiplicativity of the complete regularity in general L-fuzzy topological spaces is also answered negatively.     

Maximal regularity of second order delay equations in Banach spaces

We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(resp.Bsp ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).     

Global regularity criterion for the Navier‐Stokes equations based on the direction of vorticity

We study the regularity criterion for the Navier‐Stokes equations and show that the (β₁,β₂,β₃)‐Hölder continuity assumption in (x₁,x₂,x₃) on the direction of the vorticity ensures the regularity of the solution. This may be viewed as an extension of many previous results, since some of the β_i can be arbitrarily small.     

A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations

Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations.In this survey paper,we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space.We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.     

Castelnuovo–Mumford Regularity of Some Modules

We give bounds for the Castelnuovo–Mumford regularity of the so-called sequentially κ-Buchsbaum modules and of the canonical modules of certain rings.     

Existence and regularity of weak solutions to a model for coarsening in molecular beam epitaxy

Taking into account the occurrence of a zero of the surface diffusion current and the requirement of the Ehrlich–Schwoebel effect, Siegert et al. formulated a model of Langevin type that describes the growth of pyramid‐like structures on a surface under conditions of molecular beam epitaxy and that the slope of these pyramids is selected by the crystalline symmetries of the growing film. In this article, the existence and uniqueness of weak solution to an initial boundary value problem for this model is proved, in the case that the noise is neglected. The regularity of the weak solution to models, with/without slope selection, is also investigated. Copyright © 2012 John Wiley & Sons, Ltd.