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Cornell University

1. Tasena, Santi. Heat Kernal Analysis On Weighted Dirichlet Spaces.

Degree: PhD, Mathematics, 2011, Cornell University

This thesis is concerned with heat kernel estimates on weighted Dirichlet spaces. The Dirichlet forms considered here are strongly local and regular. They are defined on a complete locally compact separable metric space. The associated heat equation is similar to that of local divergence form differential operators. The weight functions studied have the form of a function of the distance from a closed set [SIGMA], that is, x [RIGHTWARDS ARROW] a(d( x, [SIGMA])). We place conditions on the geometry of the set [SIGMA] and the growth rate of function a itself. The function a can either blow up at 0 or [INFINITY] or both. Some results include the case where [SIGMA] separates the whole spaces. It can also apply to the case where [SIGMA] do not separate the space, for example, a domain Ω and its boundary [SIGMA] = ∂Ω. The condition on [SIGMA] is rather mild and do not assume differentiability condition. Advisors/Committee Members: Saloff-Coste, Laurent Pascal (chair), Cao, Xiaodong (committee member), Gross, Leonard (committee member).

Subjects/Keywords: poincare inequality; doubling; remotely constant

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Tasena, S. (2011). Heat Kernal Analysis On Weighted Dirichlet Spaces. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/33627

Chicago Manual of Style (16th Edition):

Tasena, Santi. “Heat Kernal Analysis On Weighted Dirichlet Spaces.” 2011. Doctoral Dissertation, Cornell University. Accessed September 29, 2020. http://hdl.handle.net/1813/33627.

MLA Handbook (7th Edition):

Tasena, Santi. “Heat Kernal Analysis On Weighted Dirichlet Spaces.” 2011. Web. 29 Sep 2020.

Vancouver:

Tasena S. Heat Kernal Analysis On Weighted Dirichlet Spaces. [Internet] [Doctoral dissertation]. Cornell University; 2011. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/1813/33627.

Council of Science Editors:

Tasena S. Heat Kernal Analysis On Weighted Dirichlet Spaces. [Doctoral Dissertation]. Cornell University; 2011. Available from: http://hdl.handle.net/1813/33627

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