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Bridging Local and Nonlocal Models: Convergence and Regularity

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Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Abstract

As nonlocal models become more widespread in applications, we focus on their connections with their classical counterparts and also on some theoretical aspects which impact their implementation. In this context we survey recent developments by the authors and prove some new results on regularity of solutions to nonlinear systems in the nonlocal framework. In particular, we focus on semilinear problems and also on higher-order problems with applications in the theory of plate deformations.

The second author acknowledges support from the Simons Foundation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, USA

    Mikil D. Foss & Petronela Radu

Authors
  1. Mikil D. Foss
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  2. Petronela Radu
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Corresponding author

Correspondence to Mikil D. Foss .

Editor information

Editors and Affiliations

  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA, USA

    George Z. Voyiadjis

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Foss, M.D., Radu, P. (2019). Bridging Local and Nonlocal Models: Convergence and Regularity. In: Voyiadjis, G. (eds) Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-58729-5_32

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