On Mosco Convergence of Diffusion Dirichlet Forms

2009 ◽  
Vol 53 (2) ◽  
pp. 242-255 ◽  
Author(s):  
O. V. Pugachev
Keyword(s):  
Dirichlet Forms ◽  
Mosco Convergence

CLOSURE OF THE SET OF DIFFUSION FUNCTIONALS WITH RESPECT TO THE MOSCO-CONVERGENCE

2002 ◽  
Vol 12 (08) ◽  
pp. 1153-1176 ◽  
Author(s):  
M. CAMAR-EDDINE ◽  
P. SEPPECHER
Keyword(s):  
Composite Material ◽  
Bounded Domain ◽  
Explicit Construction ◽  
Dirichlet Forms ◽  
Mosco Convergence ◽  
Nonlocal Interaction ◽  
Effective Energy ◽  
Closed Set ◽  
Crucial Step

We characterize the functionals which are Mosco-limits, in the L2(Ω) topology, of some sequence of functionals of the kind [Formula: see text] where Ω is a bounded domain of ℝN (N ≥ 3). It is known that this family of functionals is included in the closed set of Dirichlet forms. Here, we prove that the set of Dirichlet forms is actually the closure of the set of diffusion functionals. A crucial step is the explicit construction of a composite material whose effective energy contains a very simple nonlocal interaction.

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

scholarly journals ORLICZ–POINCARÉ INEQUALITIES

2008 ◽  
Vol 51 (2) ◽  
pp. 529-543 ◽  
Author(s):  
Feng-Yu Wang
Keyword(s):  
Porous Media ◽  
Probability Measure ◽  
Poincaré Inequality ◽  
Dirichlet Forms ◽  
Sobolev Inequalities ◽  
Young Function ◽  
Poincare Inequality ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Porous Media Equations

AbstractCorresponding to known results on Orlicz–Sobolev inequalities which are stronger than the Poincaré inequality, this paper studies the weaker Orlicz–Poincaré inequality. More precisely, for any Young function $\varPhi$ whose growth is slower than quadric, the Orlicz–Poincaré inequality$$ \|f\|_\varPhi^2\le C\E(f,f),\qquad\mu(f):=\int f\,\mathrm{d}\mu=0 $$is studied by using the well-developed weak Poincaré inequalities, where $\E$ is a conservative Dirichlet form on $L^2(\mu)$ for some probability measure $\mu$. In particular, criteria and concrete sharp examples of this inequality are presented for $\varPhi(r)=r^p$ $(p\in[1,2))$ and $\varPhi(r)= r^2\log^{-\delta}(\mathrm{e} +r^2)$ $(\delta>0)$. Concentration of measures and analogous results for non-conservative Dirichlet forms are also obtained. As an application, the convergence rate of porous media equations is described.

Non-bipartiteness of Graphs and the Upper Bounds of Dirichlet Forms

2006 ◽  
Vol 25 (3) ◽  
pp. 259-268
Author(s):  
Yusuke Higuchi ◽  
Tomoyuki Shirai
Keyword(s):  
Dirichlet Forms ◽  
Upper Bounds

scholarly journals Hardy's inequality in the scope of Dirichlet forms

2012 ◽  
Vol 24 (4) ◽  
Author(s):  
Nedra Belhadjrhouma ◽  
Ali Ben Amor
Keyword(s):  
Dirichlet Forms ◽  
Hardy’S Inequality ◽  
Hardy's Inequality
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