Abstract
The Lagrangian structure of two-dimensional integrable systems on quad-graphs is investigated. We give reality conditions under which the action functionals are strictly convex. In particular, this gives uniqueness of solutions of Dirichlet boundary value problems. In some cases, we discuss also the existence of solutions. The integrability of combinatorial data is studied. In addition, a connection between (Q3) and circle patterns is discussed.
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A.I. Bobenko is supported by the DFG Research Unit “Polyhedral Surfaces” and F. Günther is supported by the DFG Research Unit “Polyhedral Surfaces” and the Deutsche Telekom Stiftung.
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Bobenko, A.I., Günther, F. On Discrete Integrable Equations with Convex Variational Principles. Lett Math Phys 102, 181–202 (2012). https://doi.org/10.1007/s11005-012-0583-4
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DOI: https://doi.org/10.1007/s11005-012-0583-4