Search results for "obol"
showing 10 items of 228 documents
Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients
2013
In this chapter, we will explain how the Brenier’s relaxed variational principle for Euler equation makes involved the ordinary differential equations with Sobolev coefficients and how the investigation on stochastic differential equations (SDE) with Sobolev coefficients is useful to establish variational principles for Navier–Stokes equations. We will survey recent results on this topic.
Trace and density results on regular trees
2019
We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.
Local maximal operators on fractional Sobolev spaces
2016
In this note we establish the boundedness properties of local maximal operators MG on the fractional Sobolev spaces Ws;p(G) whenever G is an open set in Rn, 0 < s < 1 and 1 < p < 1. As an application, we characterize the fractional (s;p)-Hardy inequality on a bounded open set by a Maz'ya-type testing condition localized to Whitney cubes. pq(G) whenever G is an open set in R n , 0 < s < 1 and 1 < p;q <1. Our main focus lies in the mapping properties of MG on a fractional Sobolev space W s;p (G) with 0 < s < 1 and 1 < p < 1, see Section 2 for the denition or (3) for a survey of this space. The intrinsically dened function space W s;p (G) on a given domain G coincides with the trace space F s …
Spectral rigidity and invariant distributions on Anosov surfaces
2014
This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface $(M,g)$, given a smooth function $f$ on $M$ there is a distribution in the Sobolev space $H^{-1}(SM)$ that is invariant under the geodesic flow and whose projection to $M$ i…
Boundary blow-up under Sobolev mappings
2014
We prove that for mappings $W^{1,n}(B^n, \R^n),$ continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero $n$-Hausdorff measure. For H\"older continuous mappings we also prove an essentially sharp generalized Hausdorff dimension estimate.
One-dimensional nonlinear boundary value problems with variable exponent
2018
In this paper, a class of nonlinear differential boundary value problems with variable exponent is investigated. The existence of at least one non-zero solution is established, without assuming on the nonlinear term any condition either at zero or at infinity. The approach is developed within the framework of the Orlicz-Sobolev spaces with variable exponent and it is based on a local minimum theorem for differentiable functions.
Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential
2015
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.
Self-assembly of new cobalt complexes based on [Co(SCN)4], synthesis, empirical, antioxidant activity, and quantum theory investigations
2022
The cobalt (II) complexes have been synthesized from the reaction of the cationic entities (3,4-dimethylaniline (1) and histamine (2)) with metallic salt CoCl2⋅6H2O and thiocyanate ion (SCN−) as a ligand in H2O/ethanolic solution and processing by the evaporation crystal growth method at room temperature to get crystals. The synthesized complex has been fully characterized by single-crystal X-ray diffraction. UV–Visible, FTIR spectroscopy, TGA analysis, and DFT circulations were also performed. The crystal structural analysis reveals that the solid (1) {[Co(SCN)4] (C8H12N)3}·Cl crystallizes in the monoclinic system with the space group P21/n and the solid (2) {[Co(SCN)4](C5H11N3)2}·2Cl crys…
Myxosporea parasites in roach, Rutilus rutilus (Linnaeus), from four lakes in central Finland
1991
Ten myxosporean species belonging to three families were found in roach, Rutilus rutilus (Linnaeus), obtained in 1985 and 1986 from four lakes in central Finland which are connected to each other, but differ in water quality. One of the lakes is polluted by paper and pulp mill effluent, two are eutrophic and one is oligotrophic and still in its natural state. Eight species were found in all the lakes. The most common species were Myxidium rhodei Leger, 1905, Myxobolus muelleri Butschli, 1882 and Myxobolus pseudodispar Gorbunova, 1936 with prevalences varying between 66–80, 16–31 and 32–59%, respectively, in the four lakes. The largest difference in myxosporean prevalence between lakes was f…
Sharpness of the differentiability almost everywhere and capacitary estimates for Sobolev mappings
2017
We give sharp conformal conditions for the dfferentiability in the Sobolev space W1, n-1 loc (Ω,Rn). Furthermore, we show that the space W1, n-1 loc (Ω,Rn) can be considered as the borderline space for some capacitary inequalities. peerReviewed