TY  - JOUR
A1  - Hinz, Michael
A1  - Schwarz, Michael
T1  - A note on Neumann problems on graphs
JF  - Positivity
N2  - 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.
KW  - Graphs
KW  - Discrete Dirichlet forms
KW  - Neumann problem
KW  - Royden boundary
Y1  - 2022
U6  - https://doi.org/10.1007/s11117-022-00930-0
SN  - 1385-1292
SN  - 1572-9281
VL  - 26
IS  - 4
PB  - Springer
CY  - Dordrecht
ER  -