Sviridov, Alexander Petrovich
(2011)
Elliptic equations in graphs via stochastic games.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Consider a connected finite graph E with set of vertices X. Choose a nonempty subset Y ⊂ X, not equal to the whole X, and call it the boundary Y = ∂ X. We are given a real valued function F : Y → R. Our objective is to find function u on X, such that u = F on Y and u satisfies the following equation for all x ∈ X Y u(x) = α max_(y ∈ S(x)) u(y) + β min_(y ∈ S(x))u(y) + γ( ∑_(y ∈ S(x)) u(y) ⁄ #(S(x) ) , (1)where α, β, and γ are some predetermined non-negative constants such that α + β + γ = 1, for x ∈ X, #S(x) is the set of vertices connected to x by an edge, and #(S (x)) denotes the cardinality of S (x). We prove existence and uniqueness of the solution of the above Dirichlet problem and study qualitative properties of the solutions.
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Details
Item Type: |
University of Pittsburgh ETD
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Status: |
Unpublished |
Creators/Authors: |
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ETD Committee: |
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Date: |
21 July 2011 |
Date Type: |
Completion |
Defense Date: |
18 June 2010 |
Approval Date: |
21 July 2011 |
Submission Date: |
5 November 2010 |
Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
Institution: |
University of Pittsburgh |
Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
Degree: |
PhD - Doctor of Philosophy |
Thesis Type: |
Doctoral Dissertation |
Refereed: |
Yes |
Uncontrolled Keywords: |
infinity harmonic function; p-harmonic function; p-harmonious function; stochastic games; unique continuation |
Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-11052010-120535/, etd-11052010-120535 |
Date Deposited: |
10 Nov 2011 20:04 |
Last Modified: |
15 Nov 2016 13:51 |
URI: |
http://d-scholarship.pitt.edu/id/eprint/9581 |
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