Local Sobolev–Morrey estimates for nondivergence operators with drift on homogeneous groups

2013 ◽  
Vol 108 (2) ◽  
pp. 683-709 ◽  
Author(s):  
Xiaojing Feng ◽  
Pengcheng Niu
Keyword(s):  
Homogeneous Groups ◽  
Morrey Estimates

scholarly journals Weighted Sobolev–Morrey Estimates for Nondivergence Degenerate Operators with Drift on Homogeneous Groups

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2061
Author(s):  
Yuexia Hou
Keyword(s):  
Vector Fields ◽  
Real Vector ◽  
Ellipticity Condition ◽  
Homogeneous Groups ◽  
Mean Oscillation ◽  
Weighted Morrey Spaces ◽  
Uniform Ellipticity ◽  
Morrey Estimates ◽  
Degenerate Operator ◽  
Degenerate Operators

Let X0,X1,…,Xq(q<N) be real vector fields, which are left invariant on homogeneous group G, provided that X0 is homogeneous of degree two and X1,…,Xq are homogeneous of degree one. We consider the following nondivergence degenerate operator with drift L=∑i,j=1qaij(x)XiXj+a0(x)X0, where the coefficients aij(x), a0(x) belonging to vanishing mean oscillation space are bounded measurable functions. Furthermore, aij(x) satisfies the uniform ellipticity condition on Rq and a0(x)≠0. We obtain the local weighted Sobolev–Morrey estimates by applying the boundedness of commutators and interpolation inequalities on weighted Morrey spaces.

Self-monitoring and leadership in culturally heterogeneous and homogeneous groups

2003 ◽  
Author(s):  
Magdalene Hsien Chen Pua ◽  
Lynn R. Offermann ◽  
Catina M. Smith ◽  
Mary Sass ◽  
Craig R. Seal ◽  
...  
Keyword(s):  
Self Monitoring ◽  
Homogeneous Groups

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

The early stages of spontaneous forest regeneration on poor soils and continental sand dunes in northern Belgium

1983 ◽  
Vol 49 ◽  
Author(s):  
M. Van Miegroet
Keyword(s):  
Scots Pine ◽  
Age Differences ◽  
Forest Regeneration ◽  
Sand Dunes ◽  
Mixed Forest ◽  
Pedunculate Oak ◽  
White Poplar ◽  
Technical Problems ◽  
Homogeneous Groups ◽  
Invading Species

Spontaneous  natural regeneration under variable conditions on sandy soils and continental  sand dunes were analysed in 5 locations in N.E. Belgium.     The number of seedlings varies between 14.000 and 522.000/ha. The most  prominent invading species are red oak, pedunculate oak and Scots pine.    Two principal types of regeneration are recognized : homogeneous groups of  oak or pine and mixtures, predominantly composed by the same species.  Pioneers such as birch, willow, white poplar and wild black cherry do not  play an important role.    Social differentiation sets in quite early and is mainly provoked by age  differences. Therefore early silvicultural intervention is advisable. The  growth relationships between the species indicate that Scots pine is not in  danger of spontaneous elemination by other species. Because of the density  and variability of spontaneous forest regeneration, the conversion of pure  pine stands into mixed forest, using group regeneration to this end, poses no  real technical problems.

scholarly journals An analysis of COVID-19 clusters in India

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Pooja Sengupta ◽  
Bhaswati Ganguli ◽  
Sugata SenRoy ◽  
Aditya Chatterjee
Keyword(s):  
Public Health ◽  
Cluster Analysis ◽  
Population Density ◽  
Case Studies ◽  
Compartment Model ◽  
Health Interventions ◽  
Disease Spread ◽  
Second Phase ◽  
Public Health Interventions ◽  
Homogeneous Groups

Abstract Background In this study we cluster the districts of India in terms of the spread of COVID-19 and related variables such as population density and the number of specialty hospitals. Simulation using a compartment model is used to provide insight into differences in response to public health interventions. Two case studies of interest from Nizamuddin and Dharavi provide contrasting pictures of the success in curbing spread. Methods A cluster analysis of the worst affected districts in India provides insight about the similarities between them. The effects of public health interventions in flattening the curve in their respective states is studied using the individual contact SEIQHRF model, a stochastic individual compartment model which simulates disease prevalence in the susceptible, infected, recovered and fatal compartments. Results The clustering of hotspot districts provide homogeneous groups that can be discriminated in terms of number of cases and related covariates. The cluster analysis reveal that the distribution of number of COVID-19 hospitals in the districts does not correlate with the distribution of confirmed COVID-19 cases. From the SEIQHRF model for Nizamuddin we observe in the second phase the number of infected individuals had seen a multitudinous increase in the states where Nizamuddin attendees returned, increasing the risk of the disease spread. However, the simulations reveal that implementing administrative interventions, flatten the curve. In Dharavi, through tracing, tracking, testing and treating, massive breakout of COVID-19 was brought under control. Conclusions The cluster analysis performed on the districts reveal homogeneous groups of districts that can be ranked based on the burden placed on the healthcare system in terms of number of confirmed cases, population density and number of hospitals dedicated to COVID-19 treatment. The study rounds up with two important case studies on Nizamuddin basti and Dharavi to illustrate the growth curve of COVID-19 in two very densely populated regions in India. In the case of Nizamuddin, the study showed that there was a manifold increase in the risk of infection. In contrast it is seen that there was a rapid decline in the number of cases in Dharavi within a span of about one month.

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