Bridging Local and Nonlocal Models: Convergence and Regularity
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.
KeywordsNonlocal operators Classical differentiability Higher integrability Weakly integrable kernels Peridynamics
- F. Andreu-Vaillo, J.M. Mazón, J.D. Rossi, J.J. Toledo-Melero, Nonlocal Diffusion Problems. Volume 165 of Mathematical Surveys and Monographs (American Mathematical Society, Providence/Real Sociedad Matemática Española, Madrid, 2010)Google Scholar
- M. Foss, P. Radu, Differentiability and integrability properties for solutions to nonlocal equations, in New Trends in Differential Equations, Control Theory and Optimization: Proceedings of the 8th Congress of Romanian Mathematicians (World Scientific, 2016), pp. 105–119Google Scholar
- M. Foss, P. Radu, C. Wright, Regularity and existence of minimizers for nonlocal energy functionals. Differ. Integr. Equ. (2017, to appear)Google Scholar
- P. Radu, K. Wells, A state-based Laplacian: properties and convergence to its local and nonlocal counterparts (2017, Preprint)Google Scholar