A note on Neumann problems on graphs

A note on Neumann problems on graphs

We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2022-09, Vol.26 (4), Article 68
Hauptverfasser: Hinz, Michael, Schwarz, Michael
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Neumann problem
Operator Theory
Potential Theory
Representations
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Zusammenfassung:We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-022-00930-0