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Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part


 
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1. Title Title of document Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part
 
2. Creator Author's name, affiliation, country Mohammud Foondun; University of Utah
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Integro-differential operators. Harnack inequality. Heat kernel, Holder continuity
 
3. Subject Subject classification 60J35; 60J75
 
4. Description Abstract We consider the Dirichlet form given by $$ {\cal E}(f,f) = \frac{1}{2}\int_{R^d}\sum_{i,j=1}^d a_{ij}(x)\frac{\partial f(x)}{\partial x_i} \frac{\partial f(x)}{\partial x_j} dx$$ $$ + \int_{R^d \times R^d} (f(y)-f(x))^2J(x,y)dxdy.$$ Under the assumption that the ${a_{ij}}$ are symmetric and uniformly elliptic and with suitable conditions on $J$, the nonlocal part, we obtain upper and lower bounds on the heat kernel of the Dirichlet form. We also prove a Harnack inequality and a regularity theorem for functions that are harmonic with respect to $\cal E$.
 
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7. Date (YYYY-MM-DD) 2009-02-02
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/604
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-604
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
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