Trace Operators and Classification Criteria for Regular Trees

Nguyen, Khanh

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JYU dissertations

Authors

Nguyen, Khanh

Date

2021

The thesis deals with existence of traces of Sobolev functions defined on regular trees. The existence is shown to be strongly related to the isoperimetric profile of the tree under natural assumptions. Furthermore, we give classification criteria for regular trees.

Väitöskirjassa tutkitaan Sobolev-funktioiden jälkiä säännöllisten metristen puiden reunoilla. Jälkien olemassaolon osoitetaan liittyvän läheisesti puun isoperimetriseen profiiliin. Lisäksi annetaan kriteerejä säännöllisten metristen puiden luokitteluun.

ISBN

978-951-39-8795-4

Contains publications

Artikkeli I: Koskela, P., Nguyen, K. N., & Wang, Z. (2021). Trace and Density Results on Regular Trees. Potential Analysis, Early online. DOI: 10.1007/s11118-021-09907-2
Artikkeli II: Koskela, P., Nguyen, K. N., & Wang, Z. (2021). Trace Operators on Regular Trees. Analysis and Geometry in Metric Spaces, 8(1), 396-409. DOI: 10.1515/agms-2020-0117
Artikkeli III: Nguyen, K. N., & Wang, Z. (2020). Admissibility versus Ap-Conditions on Regular Trees. Analysis and Geometry in Metric Spaces, 8(1), 92-105. DOI: 10.1515/agms-2020-0110
Artikkeli IV: Nguyen, Khanh. Classification criteria for regular trees. Accepted by Annales Academiæ Scientiarum Fennicæ. Mathematica.