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Analysis and PDE on metric measure s...

University of Pittsburgh.

Analysis and PDE on metric measure spaces : = Sobolev functions and viscosity solutions.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Analysis and PDE on metric measure spaces :/
Reminder of title:	Sobolev functions and viscosity solutions.
Author:	Zhou, Xiaodan.
Description:	1 online resource (150 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
Subject:	Theoretical mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369419061

Analysis and PDE on metric measure spaces : = Sobolev functions and viscosity solutions.
Zhou, Xiaodan.

Analysis and PDE on metric measure spaces :Sobolev functions and viscosity solutions. - 1 online resource (150 pages)

Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

We study analysis and partial differential equations on metric measure spaces by investigating the properties of Sobolev functions or Sobolev mappings and studying the viscosity solutions to some partial differential equations.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369419061Subjects--Topical Terms:

1180455
Theoretical mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Analysis and PDE on metric measure spaces : = Sobolev functions and viscosity solutions.
LDR:02844ntm a2200349Ki 4500 001 909826
005 20180426091047.5
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007 cr mn||||a|a||
008 190606s2016 xx obm 000 0 eng d
020 $a 9781369419061
035 $a (MiAaPQ)AAI10298891
035 $a AAI10298891
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Zhou, Xiaodan. $3 1180791
245 1 0 $a Analysis and PDE on metric measure spaces : $b Sobolev functions and viscosity solutions.
264 0 $c 2016
300 $a 1 online resource (150 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Advisers: Piotr Hajlasz; Juan J. Manfredi.
502 $a Thesis (Ph.D.) $c University of Pittsburgh $d 2016.
504 $a Includes bibliographical references
520 $a We study analysis and partial differential equations on metric measure spaces by investigating the properties of Sobolev functions or Sobolev mappings and studying the viscosity solutions to some partial differential equations.
520 $a This manuscript consists of two parts. The first part is focused on the theory of Sobolev spaces on metric measure spaces. We investigate the continuity of Sobolev functions in the critical case in some general metric spaces including compact connected one-dimensional spaces and fractals. We also construct a large class of pathological n-dimensional spheres in Rn+1 by showing that for any Cantor set C ⊂ Rn+1 there is a topological embedding f : Sn → Rn+1 of the Sobolev class W1,n whose image contains the Cantor set C.
520 $a The second part is focused on the theory of viscosity solutions for nonlinear partial differential equations in metric spaces, including the Heisenberg group as an important special case. We study Hamilton-Jacobi equations on the Heisenberg group H and show uniqueness of viscosity solutions with exponential growth at infinity. Lipschitz and horizontal convexity preserving properties of these equations under appropriate assumptions are also investigated. In this part, we also study a recent game-theoretic approach to the viscosity solutions of various equations, including deterministic and stochastic games. Based on this interpretation, we give new proofs of convexity preserving properties of the mean curvature ow equations and normalized p-Laplace equations in the Euclidean space.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Theoretical mathematics. $3 1180455
655 7 $a Electronic books. $2 local $3 554714
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Pittsburgh. $3 1178873
773 0 $t Dissertation Abstracts International $g 78-05B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10298891 $z click for full text (PQDT)

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